Identifier
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) => 3
([(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) => 3
([(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) => 3
([(0,3),(1,2)],4) => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 3
([(0,3),(1,2),(2,3)],4) => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 3
([(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
([],0) => ([],1) => 2
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Description
The minimal order of a graph which is not an induced subgraph of the given graph.
For example, the graph with two isolated vertices is not an induced subgraph of the complete graph on three vertices.
By contrast, the minimal number of vertices of a graph which is not a subgraph of a graph is one plus the clique number St000097The order of the largest clique of the 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.