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MinimalDominatingSetCount on LabeledGraph ​

The dominating sets that stop dominating when any vertex is dropped.

On LabeledGraph

FindStat's St001302. The graph with no vertices has the empty set, so 1.

Called as CombinatorialStat(x, "MinimalDominatingSetCount"). 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 St001302

The number of minimally dominating sets of vertices of a graph.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001302 has the rest.