CenterVertexCount on LabeledGraph
The vertices whose greatest distance to another vertex is the least.
FindStat's St001342. In a disconnected graph every vertex is as far as 2n from another, so all are central. The graph with no vertices gives 0.
Called as CombinatorialStat(x, "CenterVertexCount"). 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 St001342
The number of vertices in the center of a graph.
| Object | Value |
|---|---|
([],1) | 1 |
([],2) | 2 |
([],3) | 3 |
([],4) | 4 |
([],5) | 5 |
([],6) | 6 |
([],7) | 7 |
([(0,1)],2) | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001342 has the rest.