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GraphTheory

 NumberOfSpanningTrees

 Calling Sequence NumberOfSpanningTrees(G)

Parameters

 G - graph

Description

 • The NumberOfSpanningTrees command returns the number of labeled spanning trees of G. The strategy is to evaluate the determinant of a certain matrix related to the graph. (See Introduction to Graph Theory, by Douglas B. West)

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{K3}≔\mathrm{CompleteGraph}\left(3\right)$
 ${\mathrm{K3}}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 3 vertices and 3 edge\left(s\right)}}$ (1)
 > $\mathrm{NumberOfSpanningTrees}\left(\mathrm{K3}\right)$
 ${3}$ (2)
 > $\mathrm{K4}≔\mathrm{CompleteGraph}\left(4\right)$
 ${\mathrm{K4}}{≔}{\mathrm{Graph 2: an undirected unweighted graph with 4 vertices and 6 edge\left(s\right)}}$ (3)
 > $\mathrm{NumberOfSpanningTrees}\left(\mathrm{K4}\right)$
 ${16}$ (4)