- FindStat

Your data matches 73 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St001880
(load all 2 compositions to match this statistic)

Mapping

Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00263: Lattices —join irreducibles⟶ Posets
St001880: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(2,3),(3,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(1,5),(2,3),(2,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(1,4),(1,5),(2,3),(2,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(1,5),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(1,5),(3,4),(4,2),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(3,4),(4,6),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3
([(0,3),(1,6),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,2),(2,1)],3)
 => 3

Description

The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.

Matching statistic: St001875
(load all 3 compositions to match this statistic)

Mapping

Mp00206: Posets —antichains of maximal size⟶ Lattices
St001875: Lattices ⟶ ℤResult quality: 67% ●values known / values provided: 95%●distinct values known / distinct values provided: 67%

Values

([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(2,3),(3,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => 5 = 4 + 1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(1,5),(2,3),(2,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(1,4),(1,5),(2,3),(2,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => 5 = 4 + 1
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
([(1,5),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
([(1,5),(3,4),(4,2),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(3,4),(4,6),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,3),(1,6),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ? = 4 + 1
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ? = 4 + 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ? = 4 + 1
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ? = 4 + 1
([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7 + 1
([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ? = 7 + 1
([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ? = 7 + 1
([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ? = 6 + 1
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ? = 6 + 1
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ? = 6 + 1
([(0,4),(0,6),(1,9),(3,8),(4,7),(5,3),(5,10),(6,5),(6,7),(7,10),(8,9),(9,2),(10,1),(10,8)],11)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ? = 6 + 1
([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7 + 1
([(0,6),(0,7),(1,5),(3,7),(4,3),(5,4),(5,6),(7,2)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ? = 6 + 1
([(0,6),(0,7),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(4,7)],8)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ? = 1 + 1
([(0,3),(0,6),(1,6),(1,7),(2,4),(2,5),(3,4),(3,7),(6,2),(7,5)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ? = 6 + 1
([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ? = 7 + 1
([(0,6),(0,7),(0,8),(2,17),(3,16),(4,9),(4,12),(5,10),(5,15),(6,13),(6,19),(7,13),(7,18),(8,5),(8,18),(8,19),(9,3),(9,22),(10,2),(10,21),(11,1),(12,22),(13,20),(14,11),(15,9),(15,21),(16,11),(17,14),(18,4),(18,15),(18,20),(19,10),(19,20),(20,12),(20,21),(21,17),(21,22),(22,14),(22,16)],23)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ? = 7 + 1
([(0,4),(0,5),(2,20),(3,19),(4,21),(5,6),(5,7),(5,21),(6,9),(6,17),(6,18),(7,11),(7,18),(8,12),(8,14),(9,13),(9,15),(10,1),(11,22),(12,24),(13,3),(13,23),(14,2),(14,24),(15,14),(15,23),(16,10),(17,13),(17,22),(18,8),(18,15),(18,22),(19,16),(20,10),(21,11),(21,17),(22,12),(22,23),(23,19),(23,24),(24,16),(24,20)],25)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ? = 7 + 1
([(0,7),(1,3),(1,7),(2,6),(3,4),(4,2),(4,5),(7,5),(7,6)],8)
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ? = 5 + 1
([(0,6),(0,7),(1,2),(1,7),(2,6),(4,5),(6,4),(7,3),(7,5)],8)
 => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
 => ? = 5 + 1
([(0,7),(1,3),(1,7),(3,5),(4,2),(4,6),(5,6),(7,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ? = 6 + 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(4,7),(6,7),(7,2),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ? = 6 + 1
([(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ? = 6 + 1
([(0,3),(0,7),(1,5),(1,7),(2,6),(3,4),(3,5),(5,2),(7,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ? = 6 + 1
([(0,7),(1,2),(1,7),(2,3),(2,6),(3,4),(3,5),(6,5),(7,4),(7,6)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ? = 6 + 1

Description

The number of simple modules with projective dimension at most 1.

Matching statistic: St000259

Mapping

Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 95%●distinct values known / distinct values provided: 67%

Values

([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(2,3),(3,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(1,5),(2,3),(2,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(1,4),(1,5),(2,3),(2,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(1,5),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(1,5),(3,4),(4,2),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 5
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(3,4),(4,6),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
 => ? = 4
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
 => ? = 4
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
 => ? = 4
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
 => ? = 4
([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
 => ? = 7
([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,4),(0,6),(1,9),(3,8),(4,7),(5,3),(5,10),(6,5),(6,7),(7,10),(8,9),(9,2),(10,1),(10,8)],11)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
 => ? = 7
([(0,6),(0,7),(1,5),(3,7),(4,3),(5,4),(5,6),(7,2)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(5,7)],8)
 => ? = 6
([(0,6),(0,7),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(4,7)],8)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(0,9),(1,8),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,9),(6,9),(7,9)],10)
 => ? = 1
([(0,3),(0,6),(1,6),(1,7),(2,4),(2,5),(3,4),(3,7),(6,2),(7,5)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(5,7)],8)
 => ? = 6
([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
 => ? = 7
([(0,6),(0,7),(0,8),(2,17),(3,16),(4,9),(4,12),(5,10),(5,15),(6,13),(6,19),(7,13),(7,18),(8,5),(8,18),(8,19),(9,3),(9,22),(10,2),(10,21),(11,1),(12,22),(13,20),(14,11),(15,9),(15,21),(16,11),(17,14),(18,4),(18,15),(18,20),(19,10),(19,20),(20,12),(20,21),(21,17),(21,22),(22,14),(22,16)],23)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,4),(0,5),(2,20),(3,19),(4,21),(5,6),(5,7),(5,21),(6,9),(6,17),(6,18),(7,11),(7,18),(8,12),(8,14),(9,13),(9,15),(10,1),(11,22),(12,24),(13,3),(13,23),(14,2),(14,24),(15,14),(15,23),(16,10),(17,13),(17,22),(18,8),(18,15),(18,22),(19,16),(20,10),(21,11),(21,17),(22,12),(22,23),(23,19),(23,24),(24,16),(24,20)],25)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,7),(1,3),(1,7),(2,6),(3,4),(4,2),(4,5),(7,5),(7,6)],8)
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ?
 => ? = 5
([(0,6),(0,7),(1,2),(1,7),(2,6),(4,5),(6,4),(7,3),(7,5)],8)
 => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
 => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
 => ?
 => ? = 5
([(0,7),(1,3),(1,7),(3,5),(4,2),(4,6),(5,6),(7,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,6),(1,4),(1,6),(3,5),(4,3),(4,7),(6,7),(7,2),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,7),(1,5),(1,7),(2,6),(3,4),(3,5),(5,2),(7,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,7),(1,2),(1,7),(2,3),(2,6),(3,4),(3,5),(6,5),(7,4),(7,6)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6

Description

The diameter of a connected graph. This is the greatest distance between any pair of vertices.

Matching statistic: St000778

Mapping

Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000778: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 95%●distinct values known / distinct values provided: 67%

Values

([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(2,3),(3,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 4
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(1,5),(2,3),(2,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(1,4),(1,5),(2,3),(2,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 4
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(1,5),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(1,5),(3,4),(4,2),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 5
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(3,4),(4,6),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4
([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([],8)
 => ? = 7
([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,4),(0,6),(1,9),(3,8),(4,7),(5,3),(5,10),(6,5),(6,7),(7,10),(8,9),(9,2),(10,1),(10,8)],11)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([],8)
 => ? = 7
([(0,6),(0,7),(1,5),(3,7),(4,3),(5,4),(5,6),(7,2)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(6,7)],8)
 => ? = 6
([(0,6),(0,7),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(4,7)],8)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8)],10)
 => ? = 1
([(0,3),(0,6),(1,6),(1,7),(2,4),(2,5),(3,4),(3,7),(6,2),(7,5)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(6,7)],8)
 => ? = 6
([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([],8)
 => ? = 7
([(0,6),(0,7),(0,8),(2,17),(3,16),(4,9),(4,12),(5,10),(5,15),(6,13),(6,19),(7,13),(7,18),(8,5),(8,18),(8,19),(9,3),(9,22),(10,2),(10,21),(11,1),(12,22),(13,20),(14,11),(15,9),(15,21),(16,11),(17,14),(18,4),(18,15),(18,20),(19,10),(19,20),(20,12),(20,21),(21,17),(21,22),(22,14),(22,16)],23)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,4),(0,5),(2,20),(3,19),(4,21),(5,6),(5,7),(5,21),(6,9),(6,17),(6,18),(7,11),(7,18),(8,12),(8,14),(9,13),(9,15),(10,1),(11,22),(12,24),(13,3),(13,23),(14,2),(14,24),(15,14),(15,23),(16,10),(17,13),(17,22),(18,8),(18,15),(18,22),(19,16),(20,10),(21,11),(21,17),(22,12),(22,23),(23,19),(23,24),(24,16),(24,20)],25)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,7),(1,3),(1,7),(2,6),(3,4),(4,2),(4,5),(7,5),(7,6)],8)
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ?
 => ? = 5
([(0,6),(0,7),(1,2),(1,7),(2,6),(4,5),(6,4),(7,3),(7,5)],8)
 => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
 => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
 => ?
 => ? = 5
([(0,7),(1,3),(1,7),(3,5),(4,2),(4,6),(5,6),(7,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,6),(1,4),(1,6),(3,5),(4,3),(4,7),(6,7),(7,2),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,7),(1,5),(1,7),(2,6),(3,4),(3,5),(5,2),(7,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,7),(1,2),(1,7),(2,3),(2,6),(3,4),(3,5),(6,5),(7,4),(7,6)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6

Description

The metric dimension of a graph. This is the length of the shortest vector of vertices, such that every vertex is uniquely determined by the vector of distances from these vertices.

Matching statistic: St001120

Mapping

Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St001120: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 95%●distinct values known / distinct values provided: 67%

Values

([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(2,3),(3,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(1,5),(2,3),(2,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(1,4),(1,5),(2,3),(2,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(1,5),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(1,5),(3,4),(4,2),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 5
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(3,4),(4,6),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
 => ? = 4
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
 => ? = 4
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
 => ? = 4
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
 => ? = 4
([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
 => ? = 7
([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,4),(0,6),(1,9),(3,8),(4,7),(5,3),(5,10),(6,5),(6,7),(7,10),(8,9),(9,2),(10,1),(10,8)],11)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
 => ? = 7
([(0,6),(0,7),(1,5),(3,7),(4,3),(5,4),(5,6),(7,2)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(5,7)],8)
 => ? = 6
([(0,6),(0,7),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(4,7)],8)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(0,9),(1,8),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,9),(6,9),(7,9)],10)
 => ? = 1
([(0,3),(0,6),(1,6),(1,7),(2,4),(2,5),(3,4),(3,7),(6,2),(7,5)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(5,7)],8)
 => ? = 6
([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
 => ? = 7
([(0,6),(0,7),(0,8),(2,17),(3,16),(4,9),(4,12),(5,10),(5,15),(6,13),(6,19),(7,13),(7,18),(8,5),(8,18),(8,19),(9,3),(9,22),(10,2),(10,21),(11,1),(12,22),(13,20),(14,11),(15,9),(15,21),(16,11),(17,14),(18,4),(18,15),(18,20),(19,10),(19,20),(20,12),(20,21),(21,17),(21,22),(22,14),(22,16)],23)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,4),(0,5),(2,20),(3,19),(4,21),(5,6),(5,7),(5,21),(6,9),(6,17),(6,18),(7,11),(7,18),(8,12),(8,14),(9,13),(9,15),(10,1),(11,22),(12,24),(13,3),(13,23),(14,2),(14,24),(15,14),(15,23),(16,10),(17,13),(17,22),(18,8),(18,15),(18,22),(19,16),(20,10),(21,11),(21,17),(22,12),(22,23),(23,19),(23,24),(24,16),(24,20)],25)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,7),(1,3),(1,7),(2,6),(3,4),(4,2),(4,5),(7,5),(7,6)],8)
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ?
 => ? = 5
([(0,6),(0,7),(1,2),(1,7),(2,6),(4,5),(6,4),(7,3),(7,5)],8)
 => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
 => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
 => ?
 => ? = 5
([(0,7),(1,3),(1,7),(3,5),(4,2),(4,6),(5,6),(7,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,6),(1,4),(1,6),(3,5),(4,3),(4,7),(6,7),(7,2),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,7),(1,5),(1,7),(2,6),(3,4),(3,5),(5,2),(7,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,7),(1,2),(1,7),(2,3),(2,6),(3,4),(3,5),(6,5),(7,4),(7,6)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6

Description

The length of a longest path in a graph.

Matching statistic: St001340

Mapping

Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St001340: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 95%●distinct values known / distinct values provided: 67%

Values

([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(2,3),(3,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 4
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(1,5),(2,3),(2,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(1,4),(1,5),(2,3),(2,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 4
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(1,5),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(1,5),(3,4),(4,2),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 5
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(3,4),(4,6),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4
([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([],8)
 => ? = 7
([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,4),(0,6),(1,9),(3,8),(4,7),(5,3),(5,10),(6,5),(6,7),(7,10),(8,9),(9,2),(10,1),(10,8)],11)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([],8)
 => ? = 7
([(0,6),(0,7),(1,5),(3,7),(4,3),(5,4),(5,6),(7,2)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(6,7)],8)
 => ? = 6
([(0,6),(0,7),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(4,7)],8)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8)],10)
 => ? = 1
([(0,3),(0,6),(1,6),(1,7),(2,4),(2,5),(3,4),(3,7),(6,2),(7,5)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(6,7)],8)
 => ? = 6
([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([],8)
 => ? = 7
([(0,6),(0,7),(0,8),(2,17),(3,16),(4,9),(4,12),(5,10),(5,15),(6,13),(6,19),(7,13),(7,18),(8,5),(8,18),(8,19),(9,3),(9,22),(10,2),(10,21),(11,1),(12,22),(13,20),(14,11),(15,9),(15,21),(16,11),(17,14),(18,4),(18,15),(18,20),(19,10),(19,20),(20,12),(20,21),(21,17),(21,22),(22,14),(22,16)],23)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,4),(0,5),(2,20),(3,19),(4,21),(5,6),(5,7),(5,21),(6,9),(6,17),(6,18),(7,11),(7,18),(8,12),(8,14),(9,13),(9,15),(10,1),(11,22),(12,24),(13,3),(13,23),(14,2),(14,24),(15,14),(15,23),(16,10),(17,13),(17,22),(18,8),(18,15),(18,22),(19,16),(20,10),(21,11),(21,17),(22,12),(22,23),(23,19),(23,24),(24,16),(24,20)],25)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,7),(1,3),(1,7),(2,6),(3,4),(4,2),(4,5),(7,5),(7,6)],8)
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ?
 => ? = 5
([(0,6),(0,7),(1,2),(1,7),(2,6),(4,5),(6,4),(7,3),(7,5)],8)
 => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
 => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
 => ?
 => ? = 5
([(0,7),(1,3),(1,7),(3,5),(4,2),(4,6),(5,6),(7,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,6),(1,4),(1,6),(3,5),(4,3),(4,7),(6,7),(7,2),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,7),(1,5),(1,7),(2,6),(3,4),(3,5),(5,2),(7,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,7),(1,2),(1,7),(2,3),(2,6),(3,4),(3,5),(6,5),(7,4),(7,6)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6

Description

The cardinality of a minimal non-edge isolating set of a graph. Let $\mathcal F$ be a set of graphs. A set of vertices $S$ is $\mathcal F$-isolating, if the subgraph induced by the vertices in the complement of the closed neighbourhood of $S$ does not contain any graph in $\mathcal F$. This statistic returns the cardinality of the smallest isolating set when $\mathcal F$ contains only the graph with two isolated vertices.

Matching statistic: St001512

Mapping

Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St001512: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 95%●distinct values known / distinct values provided: 67%

Values

([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(2,3),(3,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(1,5),(2,3),(2,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(1,4),(1,5),(2,3),(2,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(1,5),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(1,5),(3,4),(4,2),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 5
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(3,4),(4,6),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 3
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
 => ? = 4
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
 => ? = 4
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
 => ? = 4
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
 => ? = 4
([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
 => ? = 7
([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,4),(0,6),(1,9),(3,8),(4,7),(5,3),(5,10),(6,5),(6,7),(7,10),(8,9),(9,2),(10,1),(10,8)],11)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
 => ? = 7
([(0,6),(0,7),(1,5),(3,7),(4,3),(5,4),(5,6),(7,2)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(5,7)],8)
 => ? = 6
([(0,6),(0,7),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(4,7)],8)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(0,9),(1,8),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,9),(6,9),(7,9)],10)
 => ? = 1
([(0,3),(0,6),(1,6),(1,7),(2,4),(2,5),(3,4),(3,7),(6,2),(7,5)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(5,7)],8)
 => ? = 6
([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
 => ? = 7
([(0,6),(0,7),(0,8),(2,17),(3,16),(4,9),(4,12),(5,10),(5,15),(6,13),(6,19),(7,13),(7,18),(8,5),(8,18),(8,19),(9,3),(9,22),(10,2),(10,21),(11,1),(12,22),(13,20),(14,11),(15,9),(15,21),(16,11),(17,14),(18,4),(18,15),(18,20),(19,10),(19,20),(20,12),(20,21),(21,17),(21,22),(22,14),(22,16)],23)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,4),(0,5),(2,20),(3,19),(4,21),(5,6),(5,7),(5,21),(6,9),(6,17),(6,18),(7,11),(7,18),(8,12),(8,14),(9,13),(9,15),(10,1),(11,22),(12,24),(13,3),(13,23),(14,2),(14,24),(15,14),(15,23),(16,10),(17,13),(17,22),(18,8),(18,15),(18,22),(19,16),(20,10),(21,11),(21,17),(22,12),(22,23),(23,19),(23,24),(24,16),(24,20)],25)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,7),(1,3),(1,7),(2,6),(3,4),(4,2),(4,5),(7,5),(7,6)],8)
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ?
 => ? = 5
([(0,6),(0,7),(1,2),(1,7),(2,6),(4,5),(6,4),(7,3),(7,5)],8)
 => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
 => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
 => ?
 => ? = 5
([(0,7),(1,3),(1,7),(3,5),(4,2),(4,6),(5,6),(7,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,6),(1,4),(1,6),(3,5),(4,3),(4,7),(6,7),(7,2),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,7),(1,5),(1,7),(2,6),(3,4),(3,5),(5,2),(7,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,7),(1,2),(1,7),(2,3),(2,6),(3,4),(3,5),(6,5),(7,4),(7,6)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6

Description

The minimum rank of a graph. The minimum rank of a simple graph G is the smallest possible rank over all symmetric real matrices whose entry in row $i$ and column $j$ (for $i\neq j$) is nonzero whenever $\{i, j\}$ is an edge in $G$, and zero otherwise.

Matching statistic: St001949

Mapping

Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St001949: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 95%●distinct values known / distinct values provided: 67%

Values

([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(2,3),(3,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 4
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(1,5),(2,3),(2,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(1,4),(1,5),(2,3),(2,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 4
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(1,5),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(1,5),(3,4),(4,2),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 4
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 5
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(3,4),(4,6),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,3),(1,6),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 3
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4
([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([],8)
 => ? = 7
([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,4),(0,6),(1,9),(3,8),(4,7),(5,3),(5,10),(6,5),(6,7),(7,10),(8,9),(9,2),(10,1),(10,8)],11)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([],8)
 => ? = 7
([(0,6),(0,7),(1,5),(3,7),(4,3),(5,4),(5,6),(7,2)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(6,7)],8)
 => ? = 6
([(0,6),(0,7),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(4,7)],8)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8)],10)
 => ? = 1
([(0,3),(0,6),(1,6),(1,7),(2,4),(2,5),(3,4),(3,7),(6,2),(7,5)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(6,7)],8)
 => ? = 6
([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([],8)
 => ? = 7
([(0,6),(0,7),(0,8),(2,17),(3,16),(4,9),(4,12),(5,10),(5,15),(6,13),(6,19),(7,13),(7,18),(8,5),(8,18),(8,19),(9,3),(9,22),(10,2),(10,21),(11,1),(12,22),(13,20),(14,11),(15,9),(15,21),(16,11),(17,14),(18,4),(18,15),(18,20),(19,10),(19,20),(20,12),(20,21),(21,17),(21,22),(22,14),(22,16)],23)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,4),(0,5),(2,20),(3,19),(4,21),(5,6),(5,7),(5,21),(6,9),(6,17),(6,18),(7,11),(7,18),(8,12),(8,14),(9,13),(9,15),(10,1),(11,22),(12,24),(13,3),(13,23),(14,2),(14,24),(15,14),(15,23),(16,10),(17,13),(17,22),(18,8),(18,15),(18,22),(19,16),(20,10),(21,11),(21,17),(22,12),(22,23),(23,19),(23,24),(24,16),(24,20)],25)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7
([(0,7),(1,3),(1,7),(2,6),(3,4),(4,2),(4,5),(7,5),(7,6)],8)
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ?
 => ? = 5
([(0,6),(0,7),(1,2),(1,7),(2,6),(4,5),(6,4),(7,3),(7,5)],8)
 => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
 => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
 => ?
 => ? = 5
([(0,7),(1,3),(1,7),(3,5),(4,2),(4,6),(5,6),(7,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,6),(1,4),(1,6),(3,5),(4,3),(4,7),(6,7),(7,2),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6
([(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,3),(0,7),(1,5),(1,7),(2,6),(3,4),(3,5),(5,2),(7,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6
([(0,7),(1,2),(1,7),(2,3),(2,6),(3,4),(3,5),(6,5),(7,4),(7,6)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6

Description

The rigidity index of a graph. A base of a permutation group is a set $B$ such that the pointwise stabilizer of $B$ is trivial. For example, a base of the symmetric group on $n$ letters must contain all but one letter. This statistic yields the minimal size of a base for the automorphism group of a graph.

Matching statistic: St000258

Mapping

Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000258: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 95%●distinct values known / distinct values provided: 67%

Values

([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(2,3),(3,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 5 = 4 + 1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(1,5),(2,3),(2,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(1,4),(1,5),(2,3),(2,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 5 = 4 + 1
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(1,5),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(1,5),(3,4),(4,2),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 6 = 5 + 1
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(3,4),(4,6),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,3),(1,6),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4 + 1
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4 + 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4 + 1
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4 + 1
([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([],8)
 => ? = 7 + 1
([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7 + 1
([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7 + 1
([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6 + 1
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6 + 1
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6 + 1
([(0,4),(0,6),(1,9),(3,8),(4,7),(5,3),(5,10),(6,5),(6,7),(7,10),(8,9),(9,2),(10,1),(10,8)],11)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6 + 1
([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([],8)
 => ? = 7 + 1
([(0,6),(0,7),(1,5),(3,7),(4,3),(5,4),(5,6),(7,2)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(6,7)],8)
 => ? = 6 + 1
([(0,6),(0,7),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(4,7)],8)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8)],10)
 => ? = 1 + 1
([(0,3),(0,6),(1,6),(1,7),(2,4),(2,5),(3,4),(3,7),(6,2),(7,5)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(6,7)],8)
 => ? = 6 + 1
([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([],8)
 => ? = 7 + 1
([(0,6),(0,7),(0,8),(2,17),(3,16),(4,9),(4,12),(5,10),(5,15),(6,13),(6,19),(7,13),(7,18),(8,5),(8,18),(8,19),(9,3),(9,22),(10,2),(10,21),(11,1),(12,22),(13,20),(14,11),(15,9),(15,21),(16,11),(17,14),(18,4),(18,15),(18,20),(19,10),(19,20),(20,12),(20,21),(21,17),(21,22),(22,14),(22,16)],23)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7 + 1
([(0,4),(0,5),(2,20),(3,19),(4,21),(5,6),(5,7),(5,21),(6,9),(6,17),(6,18),(7,11),(7,18),(8,12),(8,14),(9,13),(9,15),(10,1),(11,22),(12,24),(13,3),(13,23),(14,2),(14,24),(15,14),(15,23),(16,10),(17,13),(17,22),(18,8),(18,15),(18,22),(19,16),(20,10),(21,11),(21,17),(22,12),(22,23),(23,19),(23,24),(24,16),(24,20)],25)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7 + 1
([(0,7),(1,3),(1,7),(2,6),(3,4),(4,2),(4,5),(7,5),(7,6)],8)
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ?
 => ? = 5 + 1
([(0,6),(0,7),(1,2),(1,7),(2,6),(4,5),(6,4),(7,3),(7,5)],8)
 => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
 => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
 => ?
 => ? = 5 + 1
([(0,7),(1,3),(1,7),(3,5),(4,2),(4,6),(5,6),(7,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6 + 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(4,7),(6,7),(7,2),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6 + 1
([(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6 + 1
([(0,3),(0,7),(1,5),(1,7),(2,6),(3,4),(3,5),(5,2),(7,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6 + 1
([(0,7),(1,2),(1,7),(2,3),(2,6),(3,4),(3,5),(6,5),(7,4),(7,6)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6 + 1

Description

The burning number of a graph. This is the minimum number of rounds needed to burn all vertices of a graph. In each round, the neighbours of all burned vertices are burnt. Additionally, an unburned vertex may be chosen to be burned.

Matching statistic: St000273

Mapping

Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000273: Graphs ⟶ ℤResult quality: 67% ●values known / values provided: 95%●distinct values known / distinct values provided: 67%

Values

([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(2,3),(3,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 5 = 4 + 1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(1,5),(2,3),(2,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(1,4),(1,5),(2,3),(2,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 5 = 4 + 1
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(1,5),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(1,5),(3,4),(4,2),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 5 = 4 + 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 6 = 5 + 1
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(3,4),(4,6),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,3),(1,6),(2,6),(3,5),(5,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 4 = 3 + 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4 + 1
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4 + 1
([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4 + 1
([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 4 + 1
([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([],8)
 => ? = 7 + 1
([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7 + 1
([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7 + 1
([(0,6),(1,7),(2,8),(3,9),(4,3),(4,7),(5,2),(5,10),(6,1),(6,4),(7,5),(7,9),(9,10),(10,8)],11)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6 + 1
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6 + 1
([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6 + 1
([(0,4),(0,6),(1,9),(3,8),(4,7),(5,3),(5,10),(6,5),(6,7),(7,10),(8,9),(9,2),(10,1),(10,8)],11)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6 + 1
([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([],8)
 => ? = 7 + 1
([(0,6),(0,7),(1,5),(3,7),(4,3),(5,4),(5,6),(7,2)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(6,7)],8)
 => ? = 6 + 1
([(0,6),(0,7),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(4,7)],8)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8)],10)
 => ? = 1 + 1
([(0,3),(0,6),(1,6),(1,7),(2,4),(2,5),(3,4),(3,7),(6,2),(7,5)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
 => ([(6,7)],8)
 => ? = 6 + 1
([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([],8)
 => ? = 7 + 1
([(0,6),(0,7),(0,8),(2,17),(3,16),(4,9),(4,12),(5,10),(5,15),(6,13),(6,19),(7,13),(7,18),(8,5),(8,18),(8,19),(9,3),(9,22),(10,2),(10,21),(11,1),(12,22),(13,20),(14,11),(15,9),(15,21),(16,11),(17,14),(18,4),(18,15),(18,20),(19,10),(19,20),(20,12),(20,21),(21,17),(21,22),(22,14),(22,16)],23)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7 + 1
([(0,4),(0,5),(2,20),(3,19),(4,21),(5,6),(5,7),(5,21),(6,9),(6,17),(6,18),(7,11),(7,18),(8,12),(8,14),(9,13),(9,15),(10,1),(11,22),(12,24),(13,3),(13,23),(14,2),(14,24),(15,14),(15,23),(16,10),(17,13),(17,22),(18,8),(18,15),(18,22),(19,16),(20,10),(21,11),(21,17),(22,12),(22,23),(23,19),(23,24),(24,16),(24,20)],25)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)
 => ?
 => ? = 7 + 1
([(0,7),(1,3),(1,7),(2,6),(3,4),(4,2),(4,5),(7,5),(7,6)],8)
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)
 => ?
 => ? = 5 + 1
([(0,6),(0,7),(1,2),(1,7),(2,6),(4,5),(6,4),(7,3),(7,5)],8)
 => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
 => ([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)
 => ?
 => ? = 5 + 1
([(0,7),(1,3),(1,7),(3,5),(4,2),(4,6),(5,6),(7,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6 + 1
([(0,6),(1,4),(1,6),(3,5),(4,3),(4,7),(6,7),(7,2),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6 + 1
([(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,5)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6 + 1
([(0,3),(0,7),(1,5),(1,7),(2,6),(3,4),(3,5),(5,2),(7,4),(7,6)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
 => ?
 => ? = 6 + 1
([(0,7),(1,2),(1,7),(2,3),(2,6),(3,4),(3,5),(6,5),(7,4),(7,6)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
 => ?
 => ? = 6 + 1

Description

The domination number of a graph. The domination number of a graph is given by the minimum size of a dominating set of vertices. A dominating set of vertices is a subset of the vertex set of such that every vertex is either in this subset or adjacent to an element of this subset.

The following 63 statistics, ordered by result quality, also match your data. Click on any of them to see the details.

St000482The (zero)-forcing number of a graph. St000544The cop number of a graph. St000722The number of different neighbourhoods in a graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000916The packing number of a graph. St001093The detour number of a graph. St001286The annihilation number of a graph. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001322The size of a minimal independent dominating set in a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001339The irredundance number of a graph. St001363The Euler characteristic of a graph according to Knill. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001463The number of distinct columns in the nullspace of a graph. St001829The common independence number of a graph. St000449The number of pairs of vertices of a graph with distance 4. St000528The height of a poset. St000912The number of maximal antichains in a poset. St001820The size of the image of the pop stack sorting operator. St001720The minimal length of a chain of small intervals in a lattice. St000680The Grundy value for Hackendot on posets. St000717The number of ordinal summands of a poset. St000906The length of the shortest maximal chain in a poset. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St000643The size of the largest orbit of antichains under Panyushev complementation. St000080The rank of the poset. St000287The number of connected components of a graph. St000553The number of blocks of a graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St001828The Euler characteristic of a graph. St001623The number of doubly irreducible elements of a lattice. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St001626The number of maximal proper sublattices of a lattice. St000327The number of cover relations in a poset. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St001834The number of non-isomorphic minors of a graph. St001613The binary logarithm of the size of the center of a lattice. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001881The number of factors of a lattice as a Cartesian product of lattices. St001618The cardinality of the Frattini sublattice of a lattice. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001845The number of join irreducibles minus the rank of a lattice. St001846The number of elements which do not have a complement in the lattice. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001616The number of neutral elements in a lattice. St001681The number of inclusion-wise minimal subsets of a lattice, whose meet is the bottom element. St001619The number of non-isomorphic sublattices of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices. St001833The number of linear intervals in a lattice. St001677The number of non-degenerate subsets of a lattice whose meet is the bottom element. St001620The number of sublattices of a lattice. St001679The number of subsets of a lattice whose meet is the bottom element. St000909The number of maximal chains of maximal size in a poset. St000070The number of antichains in a poset. St000455The second largest eigenvalue of a graph if it is integral. St001733The number of weak left to right maxima of a Dyck path. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path.