SpanningTreeCount on LabeledGraph

The spanning trees: by the matrix-tree theorem, the determinant of the Laplacian with its last row and column deleted.

On LabeledGraph

FindStat's St000096. A graph with two components has none. The graph with no vertices gives 0.

Called as CombinatorialStat(x, "SpanningTreeCount"). 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.

Sizes 1 to

FindStat St000096

The number of spanning trees of a graph.

The number of spanning trees of a graph. A subgraph $H \subseteq G$ is a spanning tree if $V(H)=V(G)$ and $H$ is a tree (i.e. $H$ is connected and contains no cycles).

Object	Value
([],1)	1
([],2)	0
([],3)	0
([],4)	0
([],5)	0
([],6)	0
([(0,1)],2)	1
([(1,2)],3)	0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000096 has the rest.