Identifier
Values
([],1) => ([],1) => ([(0,1)],2) => 1
([],2) => ([],1) => ([(0,1)],2) => 1
([(0,1)],2) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([],3) => ([],1) => ([(0,1)],2) => 1
([(1,2)],3) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,2),(1,2)],3) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([],4) => ([],1) => ([(0,1)],2) => 1
([(2,3)],4) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,3),(2,3)],4) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,3),(1,2)],4) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,3),(1,2),(2,3)],4) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([],5) => ([],1) => ([(0,1)],2) => 1
([(3,4)],5) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(2,4),(3,4)],5) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,4),(2,3)],5) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,1),(2,4),(3,4)],5) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,1),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(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) => 5
([],6) => ([],1) => ([(0,1)],2) => 1
([(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(3,5),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(2,5),(3,4)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,2),(3,5),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,1),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,4),(2,3)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,5),(2,4),(3,4),(3,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,1),(2,5),(3,4),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,2),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
>>> Load all 204 entries. <<<
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(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) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(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) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(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) => 5
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(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) => 5
([(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(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) => 5
([(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(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) => 5
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(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) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(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) => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(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) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(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) => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(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) => 5
([(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) => ([(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) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(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) => 6
([],0) => ([],0) => ([],1) => 0
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Description
The largest eigenvalue of a graph if it is integral.
If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
Map
cone
Description
The cone of a graph.
The cone of a graph is obtained by joining a new vertex to all the vertices of the graph. The added vertex is called a universal vertex or a dominating vertex.
Map
core
Description
The core of a graph.
The core of a graph $G$ is the smallest graph $C$ such that there is a homomorphism from $G$ to $C$ and a homomorphism from $C$ to $G$.
Note that the core of a graph is not necessarily connected, see [2].