The SpanningTree command returns a spanning tree of G, a subgraph that contains all the vertices and is a tree. Edge weights are ignored.

To compute a minimal-weight spanning tree for a weighted graph, use MinimalSpanningTree.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{with}\left(\mathrm{SpecialGraphs}\right)\:$

$P≔\mathrm{PetersenGraph}\left(\right)$

$P≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 10\; vertices\; and\; 15\; edge(s)}$

$\mathrm{T1}≔\mathrm{SpanningTree}\left(P\right)$

$\mathrm{T1}≔\mathrm{Graph\; 2:\; an\; undirected\; unweighted\; graph\; with\; 10\; vertices\; and\; 9\; edge(s)}$

$\mathrm{IsTree}\left(\mathrm{T1}\right)$

$\mathrm{true}$

$\mathrm{DrawGraph}\left(P\right)$

$\mathrm{DrawGraph}\left(\mathrm{T1}\right)$

$\mathrm{T2}≔\mathrm{SpanningTree}\left(P\,5\right)\:$

$\mathrm{Edges}\left(\mathrm{T1}\right)$

$\left\{\left\{1\,2\right\}\,\left\{1\,5\right\}\,\left\{1\,6\right\}\,\left\{2\,3\right\}\,\left\{2\,9\right\}\,\left\{4\,5\right\}\,\left\{5\,8\right\}\,\left\{6\,7\right\}\,\left\{6\,10\right\}\right\}$

$\mathrm{Edges}\left(\mathrm{T2}\right)$

$\left\{\left\{1\,2\right\}\,\left\{1\,5\right\}\,\left\{1\,6\right\}\,\left\{3\,4\right\}\,\left\{4\,5\right\}\,\left\{4\,10\right\}\,\left\{5\,8\right\}\,\left\{7\,8\right\}\,\left\{8\,9\right\}\right\}$