EulerFaceCount on LabeledGraph
The edges less the vertices plus 2: the faces of a connected planar graph.
FindStat's St000450. The graph with no vertices gives 2, the formula as written.
Called as CombinatorialStat(x, "EulerFaceCount"). The head's page has its examples.
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FindStat St000450
The number of edges minus the number of vertices plus 2 of a graph.
| Object | Value |
|---|---|
([],1) | 1 |
([],2) | 0 |
([],3) | -1 |
([],4) | -2 |
([],5) | -3 |
([],6) | -4 |
([(0,1)],2) | 1 |
([(1,2)],3) | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000450 has the rest.