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GraphVertexConnectivity on LabeledGraph ​

The fewest vertices whose deletion leaves a disconnected graph; the complete graph on n vertices gives n - 1.

On LabeledGraph

FindStat's St000262. A disconnected graph gives 0. The graph with no vertices gives 0.

Called as CombinatorialStat(x, "GraphVertexConnectivity"). The head's page has its examples.

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Distribution

Over LabeledGraphs at each size, tallied here in your browser; sizes past 6 are not offered.

FindStat St000262

The vertex connectivity of a graph.

ObjectValue
([],1)0
([],2)0
([],3)0
([],4)0
([],5)0
([],6)0
([(0,1)],2)1
([(1,2)],3)0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000262 has the rest.