- FindStat

Identifier

St001738: Graphs ⟶ ℤ

Values

=>
                            Cc0020;cc-rep
                            
                            
                            

                        ([],0)=>1
([],1)=>2
([],2)=>2
([(0,1)],2)=>2
([],3)=>2
([(1,2)],3)=>3
([(0,2),(1,2)],3)=>3
([(0,1),(0,2),(1,2)],3)=>2
([],4)=>2
([(2,3)],4)=>3
([(1,3),(2,3)],4)=>3
([(0,3),(1,3),(2,3)],4)=>3
([(0,3),(1,2)],4)=>3
([(0,3),(1,2),(2,3)],4)=>3
([(1,2),(1,3),(2,3)],4)=>3
([(0,3),(1,2),(1,3),(2,3)],4)=>3
([(0,2),(0,3),(1,2),(1,3)],4)=>3
([(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)=>2
([],5)=>2
([(3,4)],5)=>3
([(2,4),(3,4)],5)=>3
([(1,4),(2,4),(3,4)],5)=>3
([(0,4),(1,4),(2,4),(3,4)],5)=>3
([(1,4),(2,3)],5)=>3
([(1,4),(2,3),(3,4)],5)=>3
([(0,1),(2,4),(3,4)],5)=>3
([(2,3),(2,4),(3,4)],5)=>3
([(0,4),(1,4),(2,3),(3,4)],5)=>3
([(1,4),(2,3),(2,4),(3,4)],5)=>4
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
([(1,3),(1,4),(2,3),(2,4)],5)=>3
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>3
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>4
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
([(0,4),(1,3),(2,3),(2,4)],5)=>3
([(0,1),(2,3),(2,4),(3,4)],5)=>3
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>3
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>3
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>3
([(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),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>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..

Code

def statistic(G):
    for n in range(1, G.num_verts()+2):
        for H in graphs(n):
            if not G.subgraph_search(H, induced=True):
                return n

Created

Sep 13, 2021 at 11:13 by Martin Rubey

Updated

Sep 13, 2021 at 11:13 by Martin Rubey