Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000422
(load all 6 compositions to match this statistic)
Mapping
Mp00074: Posets —to graph⟶ Graphs
St000422: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => 0
([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],3)
 => 0
([(1,2)],3)
 => ([(1,2)],3)
 => 2
([],4)
 => ([],4)
 => 0
([(2,3)],4)
 => ([(2,3)],4)
 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 4
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
([],5)
 => ([],5)
 => 0
([(3,4)],5)
 => ([(3,4)],5)
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 4
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => 4
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 4
([],6)
 => ([],6)
 => 0
([(4,5)],6)
 => ([(4,5)],6)
 => 2
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 4
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 6
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => 6
([(2,3),(2,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => 4
([(1,5),(5,2),(5,3),(5,4)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 4
([(1,5),(2,5),(5,3),(5,4)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 4
([(1,5),(2,5),(3,5),(5,4)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 4
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 4
([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 6
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 6
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 6
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => 8
([(0,5),(1,5),(2,3),(3,4),(3,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 6
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 6
([(2,5),(3,4)],6)
 => ([(2,5),(3,4)],6)
 => 4
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => 4
([(0,4),(0,5),(1,4),(1,5),(2,3)],6)
 => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => 6
([(0,5),(1,2),(1,3),(1,5),(5,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 6
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => 8
([(0,4),(1,2),(1,3),(2,5),(3,5)],6)
 => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => 6
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => 6
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => 8
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => 8
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => 8
([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => 8
([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 6
([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 6
([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => 6
Description
The energy of a graph, if it is integral. The energy of a graph is the sum of the absolute values of its eigenvalues. This statistic is only defined for graphs with integral energy. It is known, that the energy is never an odd integer [2]. In fact, it is never the square root of an odd integer [3]. The energy of a graph is the sum of the energies of the connected components of a graph. The energy of the complete graph $K_n$ equals $2n-2$. For this reason, we do not define the energy of the empty graph.
Matching statistic: St000264
(load all 2 compositions to match this statistic)
Mapping
Mp00074: Posets —to graph⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
Mp00157: Graphs —connected complement⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 20% ●values known / values provided: 31%●distinct values known / distinct values provided: 20%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => ? = 0 - 5
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => ? = 0 - 5
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 2 - 5
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => ? = 0 - 5
([(1,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 2 - 5
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => ? = 0 - 5
([(2,3)],4)
 => ([(2,3)],4)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 2 - 5
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 4 - 5
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ? = 4 - 5
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 4 - 5
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => ? = 0 - 5
([(3,4)],5)
 => ([(3,4)],5)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 2 - 5
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 4 - 5
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 4 - 5
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 4 - 5
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 4 - 5
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 4 - 5
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 4 - 5
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ? = 4 - 5
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 4 - 5
([],6)
 => ([],6)
 => ([],1)
 => ([],1)
 => ? = 0 - 5
([(4,5)],6)
 => ([(4,5)],6)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 2 - 5
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 4 - 5
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 6 - 5
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 6 - 5
([(2,3),(2,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 4 - 5
([(1,5),(5,2),(5,3),(5,4)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 4 - 5
([(1,5),(2,5),(5,3),(5,4)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 4 - 5
([(1,5),(2,5),(3,5),(5,4)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 4 - 5
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 4 - 5
([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 6 - 5
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 6 - 5
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 6 - 5
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 3 = 8 - 5
([(0,5),(1,5),(2,3),(3,4),(3,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 6 - 5
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 6 - 5
([(2,5),(3,4)],6)
 => ([(2,5),(3,4)],6)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ? = 4 - 5
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 4 - 5
([(0,4),(0,5),(1,4),(1,5),(2,3)],6)
 => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ? = 6 - 5
([(0,5),(1,2),(1,3),(1,5),(5,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 6 - 5
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 3 = 8 - 5
([(0,4),(1,2),(1,3),(2,5),(3,5)],6)
 => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ? = 6 - 5
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 6 - 5
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 3 = 8 - 5
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 3 = 8 - 5
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 3 = 8 - 5
([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 3 = 8 - 5
([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 6 - 5
([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 6 - 5
([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ? = 6 - 5
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 3 = 8 - 5
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? = 6 - 5
([],7)
 => ([],7)
 => ([],1)
 => ([],1)
 => ? = 0 - 5
([(5,6)],7)
 => ([(5,6)],7)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 2 - 5
([(2,3),(2,4),(2,5),(2,6)],7)
 => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 4 - 5
([(1,4),(1,5),(1,6),(6,2),(6,3)],7)
 => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ? = 6 - 5
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => ? = 6 - 5
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => 3 = 8 - 5
([(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => 3 = 8 - 5
([(1,4),(1,5),(2,3),(2,5),(3,6),(4,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => 3 = 8 - 5
([(1,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => 3 = 8 - 5
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => 3 = 8 - 5
([(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => 3 = 8 - 5
([(0,6),(1,5),(2,3),(2,5),(2,6),(3,4)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => 3 = 8 - 5
([(0,3),(0,6),(4,2),(5,1),(6,4),(6,5)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(0,6),(1,3),(1,5),(4,2),(5,4),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(0,6),(1,5),(2,3),(2,4),(4,5),(4,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(0,4),(0,6),(1,3),(1,6),(5,2),(6,5)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(0,6),(1,4),(1,5),(2,3),(2,5),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(0,5),(1,4),(1,6),(2,3),(2,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(0,4),(1,3),(1,6),(4,6),(5,2),(6,5)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(0,5),(1,4),(2,3),(2,6),(4,6),(6,5)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(0,5),(1,4),(2,3),(2,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(0,6),(1,4),(3,2),(4,5),(5,3),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
([(0,6),(1,5),(2,3),(3,4),(4,5),(4,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 3 = 8 - 5
Description
The girth of a graph, which is not a tree. This is the length of the shortest cycle in the graph.