Values
([],1) => ([(0,1)],2) => 2
([],2) => ([(0,2),(1,2)],3) => 3
([(0,1)],2) => ([(0,1),(0,2),(1,2)],3) => 2
([],3) => ([(0,3),(1,3),(2,3)],4) => 4
([(1,2)],3) => ([(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,2),(1,2)],3) => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
([],4) => ([(0,4),(1,4),(2,4),(3,4)],5) => 5
([(2,3)],4) => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(1,3),(2,3)],4) => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,3),(1,3),(2,3)],4) => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(0,3),(1,2)],4) => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 4
([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 4
([(1,2),(1,3),(2,3)],4) => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
([(0,3),(1,2),(1,3),(2,3)],4) => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
([(0,2),(0,3),(1,2),(1,3)],4) => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 3
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
([(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) => 2
([],5) => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 6
([(3,4)],5) => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(2,4),(3,4)],5) => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(1,4),(2,4),(3,4)],5) => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(1,4),(2,3)],5) => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 5
([(1,4),(2,3),(3,4)],5) => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(0,1),(2,4),(3,4)],5) => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(2,3),(2,4),(3,4)],5) => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(1,4),(2,3),(2,4),(3,4)],5) => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
([(1,3),(1,4),(2,3),(2,4)],5) => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 4
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 4
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(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) => 4
([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 5
([(0,1),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 4
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => ([(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) => 4
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],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) => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],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) => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => ([(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) => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => ([(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) => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => ([(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) => 3
([(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) => 2
([],6) => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 7
([(4,5)],6) => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(3,5),(4,5)],6) => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(2,5),(3,5),(4,5)],6) => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(1,5),(2,5),(3,5),(4,5)],6) => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(2,5),(3,4)],6) => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 6
([(2,5),(3,4),(4,5)],6) => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(1,2),(3,5),(4,5)],6) => ([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(3,4),(3,5),(4,5)],6) => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(1,5),(2,5),(3,4),(4,5)],6) => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(0,1),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(2,5),(3,4),(3,5),(4,5)],6) => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(2,4),(2,5),(3,4),(3,5)],6) => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 5
([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 6
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 5
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 5
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 5
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,6),(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) => 5
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,5),(0,6),(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) => 5
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 5
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,4),(0,5),(0,6),(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) => 5
([(0,5),(1,4),(2,3)],6) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => 6
([(1,5),(2,4),(3,4),(3,5)],6) => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 6
([(0,1),(2,5),(3,4),(4,5)],6) => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(1,2),(3,4),(3,5),(4,5)],6) => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 5
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
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Description
The number of vertices of the largest induced subforest of a graph.
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.
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.
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