Identifier
Values
([(0,1)],2) => [1,1] => [1,1] => ([(0,1)],2) => -1
([(1,2)],3) => [2,1] => [1,2] => ([(1,2)],3) => 0
([(0,2),(1,2)],3) => [2,1] => [1,2] => ([(1,2)],3) => 0
([(0,1),(0,2),(1,2)],3) => [1,1,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => -1
([(2,3)],4) => [3,1] => [1,3] => ([(2,3)],4) => 0
([(1,3),(2,3)],4) => [3,1] => [1,3] => ([(2,3)],4) => 0
([(0,3),(1,3),(2,3)],4) => [3,1] => [1,3] => ([(2,3)],4) => 0
([(0,3),(1,2)],4) => [2,2] => [2,2] => ([(1,3),(2,3)],4) => 0
([(0,3),(1,2),(2,3)],4) => [2,2] => [2,2] => ([(1,3),(2,3)],4) => 0
([(0,2),(0,3),(1,2),(1,3)],4) => [2,2] => [2,2] => ([(1,3),(2,3)],4) => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [1,1,1,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => -1
([(3,4)],5) => [4,1] => [1,4] => ([(3,4)],5) => 0
([(2,4),(3,4)],5) => [4,1] => [1,4] => ([(3,4)],5) => 0
([(1,4),(2,4),(3,4)],5) => [4,1] => [1,4] => ([(3,4)],5) => 0
([(0,4),(1,4),(2,4),(3,4)],5) => [4,1] => [1,4] => ([(3,4)],5) => 0
([(1,4),(2,3)],5) => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 0
([(1,4),(2,3),(3,4)],5) => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 0
([(0,1),(2,4),(3,4)],5) => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 0
([(0,4),(1,4),(2,3),(3,4)],5) => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 0
([(1,3),(1,4),(2,3),(2,4)],5) => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 0
([(0,4),(1,3),(2,3),(2,4)],5) => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 0
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [1,1,1,1,1] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => -1
([(4,5)],6) => [5,1] => [1,5] => ([(4,5)],6) => 0
([(3,5),(4,5)],6) => [5,1] => [1,5] => ([(4,5)],6) => 0
([(2,5),(3,5),(4,5)],6) => [5,1] => [1,5] => ([(4,5)],6) => 0
([(1,5),(2,5),(3,5),(4,5)],6) => [5,1] => [1,5] => ([(4,5)],6) => 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [5,1] => [1,5] => ([(4,5)],6) => 0
([(2,5),(3,4)],6) => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 0
([(2,5),(3,4),(4,5)],6) => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 0
([(1,2),(3,5),(4,5)],6) => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 0
([(1,5),(2,5),(3,4),(4,5)],6) => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 0
([(0,1),(2,5),(3,5),(4,5)],6) => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 0
([(2,4),(2,5),(3,4),(3,5)],6) => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,4),(3,4)],6) => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 0
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 0
([(0,5),(1,4),(2,3)],6) => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
([(1,5),(2,4),(3,4),(3,5)],6) => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 0
([(0,1),(2,5),(3,4),(4,5)],6) => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 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) => [1,1,1,1,1,1] => [1,1,1,1,1,1] => ([(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
([(5,6)],7) => [6,1] => [1,6] => ([(5,6)],7) => 0
([(4,6),(5,6)],7) => [6,1] => [1,6] => ([(5,6)],7) => 0
([(3,6),(4,6),(5,6)],7) => [6,1] => [1,6] => ([(5,6)],7) => 0
([(2,6),(3,6),(4,6),(5,6)],7) => [6,1] => [1,6] => ([(5,6)],7) => 0
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1] => [1,6] => ([(5,6)],7) => 0
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1] => [1,6] => ([(5,6)],7) => 0
([(3,6),(4,5)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(3,6),(4,5),(5,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(2,3),(4,6),(5,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(2,6),(3,6),(4,5),(5,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(1,2),(3,6),(4,6),(5,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(3,5),(3,6),(4,5),(4,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(1,6),(2,6),(3,5),(4,5)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(1,6),(2,5),(3,4)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(2,6),(3,5),(4,5),(4,6)],7) => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 0
([(1,2),(3,6),(4,5),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,3),(1,2),(4,6),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
>>> Load all 147 entries. <<<
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
([(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) => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => ([(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) => -1
search for individual values
searching the database for the individual values of this statistic
Description
The second largest eigenvalue of a graph if it is integral.
This statistic is undefined if the second largest eigenvalue of the graph is not integral.
Chapter 4 of [1] provides lots of context.
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to threshold graph
Description
The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
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chromatic difference sequence
Description
The chromatic difference sequence of a graph.
Let $G$ be a simple graph with chromatic number $\kappa$. Let $\alpha_m$ be the maximum number of vertices in a $m$-colorable subgraph of $G$. Set $\delta_m=\alpha_m-\alpha_{m-1}$. The sequence $\delta_1,\delta_2,\dots\delta_\kappa$ is the chromatic difference sequence of $G$.
All entries of the chromatic difference sequence are positive: $\alpha_m > \alpha_{m-1}$ for $m < \kappa$, because we can assign any uncolored vertex of a partial coloring with $m-1$ colors the color $m$. Therefore, the chromatic difference sequence is a composition of the number of vertices of $G$ into $\kappa$ parts.
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rotate back to front
Description
The back to front rotation of an integer composition.