Identifier
Values
([],1) => ([],2) => 0
([],2) => ([],3) => 0
([(0,1)],2) => ([(1,2)],3) => 0
([],3) => ([],4) => 0
([(1,2)],3) => ([(2,3)],4) => 0
([(0,2),(1,2)],3) => ([(1,3),(2,3)],4) => 0
([(0,1),(0,2),(1,2)],3) => ([(1,2),(1,3),(2,3)],4) => 0
([],4) => ([],5) => 0
([(2,3)],4) => ([(3,4)],5) => 0
([(1,3),(2,3)],4) => ([(2,4),(3,4)],5) => 0
([(0,3),(1,3),(2,3)],4) => ([(1,4),(2,4),(3,4)],5) => 0
([(0,3),(1,2)],4) => ([(1,4),(2,3)],5) => 0
([(0,3),(1,2),(2,3)],4) => ([(1,4),(2,3),(3,4)],5) => 0
([(1,2),(1,3),(2,3)],4) => ([(2,3),(2,4),(3,4)],5) => 0
([(0,3),(1,2),(1,3),(2,3)],4) => ([(1,4),(2,3),(2,4),(3,4)],5) => 0
([(0,2),(0,3),(1,2),(1,3)],4) => ([(1,3),(1,4),(2,3),(2,4)],5) => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
([],5) => ([],6) => 0
([(3,4)],5) => ([(4,5)],6) => 0
([(2,4),(3,4)],5) => ([(3,5),(4,5)],6) => 0
([(1,4),(2,4),(3,4)],5) => ([(2,5),(3,5),(4,5)],6) => 0
([(0,4),(1,4),(2,4),(3,4)],5) => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
([(1,4),(2,3)],5) => ([(2,5),(3,4)],6) => 0
([(1,4),(2,3),(3,4)],5) => ([(2,5),(3,4),(4,5)],6) => 0
([(0,1),(2,4),(3,4)],5) => ([(1,2),(3,5),(4,5)],6) => 0
([(2,3),(2,4),(3,4)],5) => ([(3,4),(3,5),(4,5)],6) => 0
([(0,4),(1,4),(2,3),(3,4)],5) => ([(1,5),(2,5),(3,4),(4,5)],6) => 0
([(1,4),(2,3),(2,4),(3,4)],5) => ([(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(1,3),(1,4),(2,3),(2,4)],5) => ([(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(1,3),(2,3),(2,4)],5) => ([(1,5),(2,4),(3,4),(3,5)],6) => 0
([(0,1),(2,3),(2,4),(3,4)],5) => ([(1,2),(3,4),(3,5),(4,5)],6) => 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 0
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([],6) => ([],7) => 0
([(4,5)],6) => ([(5,6)],7) => 0
([(3,5),(4,5)],6) => ([(4,6),(5,6)],7) => 0
([(2,5),(3,5),(4,5)],6) => ([(3,6),(4,6),(5,6)],7) => 0
([(1,5),(2,5),(3,5),(4,5)],6) => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
([(2,5),(3,4)],6) => ([(3,6),(4,5)],7) => 0
([(2,5),(3,4),(4,5)],6) => ([(3,6),(4,5),(5,6)],7) => 0
([(1,2),(3,5),(4,5)],6) => ([(2,3),(4,6),(5,6)],7) => 0
([(3,4),(3,5),(4,5)],6) => ([(4,5),(4,6),(5,6)],7) => 0
([(1,5),(2,5),(3,4),(4,5)],6) => ([(2,6),(3,6),(4,5),(5,6)],7) => 0
([(0,1),(2,5),(3,5),(4,5)],6) => ([(1,2),(3,6),(4,6),(5,6)],7) => 0
([(2,5),(3,4),(3,5),(4,5)],6) => ([(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(2,4),(2,5),(3,4),(3,5)],6) => ([(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,5),(1,5),(2,4),(3,4)],6) => ([(1,6),(2,6),(3,5),(4,5)],7) => 0
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 0
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 0
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,4),(2,3)],6) => ([(1,6),(2,5),(3,4)],7) => 0
([(1,5),(2,4),(3,4),(3,5)],6) => ([(2,6),(3,5),(4,5),(4,6)],7) => 0
([(0,1),(2,5),(3,4),(4,5)],6) => ([(1,2),(3,6),(4,5),(5,6)],7) => 0
([(1,2),(3,4),(3,5),(4,5)],6) => ([(2,3),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 0
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 0
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 0
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 0
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 0
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 0
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => 0
>>> Load all 208 entries. <<<
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => 0
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => 0
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 0
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => ([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7) => 0
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => ([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 0
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => ([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => 0
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => 0
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 0
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => ([(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => 0
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 0
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 0
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 0
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => 0
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 0
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => 0
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 0
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 0
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => 0
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => ([(1,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => 0
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => ([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => 0
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 0
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => ([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7) => 0
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => ([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 0
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) => ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => 0
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 0
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 0
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 0
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 0
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 0
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 0
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The determinant of the adjacency matrix of a graph.
For a labelled graph $G$ with vertices $\{1,\ldots,n\}$, the adjacency matrix is the matrix $(a_{ij})$ with $a_{ij} = 1$ if the vertices $i$ and $j$ are joined by an edge in $G$.
Since the determinant is invariant under simultaneous row and column permutations, the determinant of the adjacency is well-defined for an unlabelled graph.
According to [2], Equation 8, this determinant can be computed as follows: let $s(G)$ be the number of connected components of $G$ that are cycles and $r(G)$ the number of connected components that equal $K_2$. Then $$\det(A) = \sum_{H} (-1)^{r(H)} 2^{s(H)}$$ where the sum is over all spanning subgraphs $H$ of $G$ that have as connected components only $K_2$'s and cycles.
Map
vertex addition
Description
Adds a disconnected vertex to a graph.