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DominationNumber on LabeledGraph ​

The fewest vertices such that every vertex is one of them or adjacent to one.

On LabeledGraph

FindStat's St000273. The graph with no vertices gives 0.

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

Live

Distribution

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

FindStat St000273

The domination number of a graph.

ObjectValue
([],1)1
([],2)2
([],3)3
([],4)4
([],5)5
([],6)6
([],7)7
([(0,1)],2)1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000273 has the rest.