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SmallestMissingDegree on LabeledGraph ​

The least number, 0 or more, that is not the degree of any vertex.

On LabeledGraph

FindStat's St001367. The graph with no vertices gives 0.

Called as CombinatorialStat(x, "SmallestMissingDegree"). 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 St001367

The smallest number which does not occur as degree of a vertex in a graph.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001367 has the rest.