Identifier
-
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St001060: Graphs ⟶ ℤ
Values
[1,0,1,1,0,1,0,0] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,0,1,0,0,1,0] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => ([(1,5),(2,4),(3,4),(3,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => ([(1,5),(2,4),(3,4),(3,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => ([(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => ([(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => ([(1,5),(2,4),(3,4),(3,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,6,2,4,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => ([(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,2,5,6,3] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => ([(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => ([(1,5),(2,4),(3,4),(3,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,1,5,6,2,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,1,5,2,3,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,5,1,6,2,3] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,2,6,3,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,1,6,2,3,5] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => ([(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => ([(1,5),(2,5),(3,4),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(3,4)],5) => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,1,2,6,3,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [5,1,6,2,3,4] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,5,7,1,6] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,4,6,1,7,5] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,4,6,7,1,5] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,4,6,1,5,7] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(1,4),(2,3),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,4,7,1,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,3,5,1,6,7,4] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,3,5,1,6,4,7] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(1,5),(2,4),(3,4),(3,5)],6) => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,3,5,6,1,7,4] => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,5,6,7,1,4] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,6,1,4,7] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => ([(1,4),(2,3),(3,4)],5) => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,5,1,7,4,6] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,7,1,4,6] => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,1,4,6,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => ([(1,4),(2,3),(3,4)],5) => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,3,6,1,4,7,5] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,6,1,7,4,5] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,6,7,1,4,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,6,1,4,5,7] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(1,4),(2,3),(3,4)],5) => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,7,1,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,4,1,5,6,7,3] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,4,1,5,6,3,7] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(1,5),(2,4),(3,4),(3,5)],6) => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,4,1,5,3,6,7] => ([(2,6),(3,5),(4,5),(4,6)],7) => ([(1,5),(2,4),(3,4),(3,5)],6) => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,5,1,6,7,3] => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
>>> Load all 292 entries. <<<
search for individual values
searching the database for the individual values of this statistic
Description
The distinguishing index of a graph.
This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism.
If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.
This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism.
If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of {1,…,n}, this is the graph with vertices {1,…,n}, where (i,j) is an edge if and only if it is an inversion of the permutation.
For a permutation of {1,…,n}, this is the graph with vertices {1,…,n}, where (i,j) is an edge if and only if it is an inversion of the permutation.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
de-duplicate
Description
The de-duplicate of a graph.
Let G=(V,E) be a graph. This map yields the graph whose vertex set is the set of (distinct) neighbourhoods {Nv|v∈V} of G, and has an edge (Na,Nb) between two vertices if and only if (a,b) is an edge of G. This is well-defined, because if Na=Nc and Nb=Nd, then (a,b)∈E if and only if (c,d)∈E.
The image of this map is the set of so-called 'mating graphs' or 'point-determining graphs'.
This map preserves the chromatic number.
Let G=(V,E) be a graph. This map yields the graph whose vertex set is the set of (distinct) neighbourhoods {Nv|v∈V} of G, and has an edge (Na,Nb) between two vertices if and only if (a,b) is an edge of G. This is well-defined, because if Na=Nc and Nb=Nd, then (a,b)∈E if and only if (c,d)∈E.
The image of this map is the set of so-called 'mating graphs' or 'point-determining graphs'.
This map preserves the chromatic number.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!