decomposition : keyword option of the form decomposition=true or decomposition=false. This specifies whether the decomposition into a maximum clique and an independent set should be returned when the graph is a split graph. The default is false.

The IsSplitGraph(G) command returns true if G is a split graph and false otherwise.

An undirected graph G is a split graph if its vertices can be partitioned into a clique and an independent set. The partition is in general not unique. Split graphs are closed under complement.

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

$K≔\mathrm{Graph}\left(5\,\left\{\left\{1\,2\right\}\,\left\{1\,3\right\}\,\left\{2\,3\right\}\,\left\{2\,4\right\}\,\left\{3\,4\right\}\,\left\{4\,5\right\}\right\}\right)$

$K≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 5\; vertices\; and\; 6\; edge(s)}$

$\mathrm{IsSplitGraph}\left(K\right)$

$\mathrm{true}$

$\mathrm{IsSplitGraph}\left(K\,\mathrm{decomposition}\right)$

$\mathrm{true},\left[\left[2\,3\,4\right]\,\left[1\,5\right]\right]$

$P≔\mathrm{PathGraph}\left(4\right)$

$P≔\mathrm{Graph\; 2:\; an\; undirected\; unweighted\; graph\; with\; 4\; vertices\; and\; 3\; edge(s)}$

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

$\mathrm{true}$

$\mathrm{IsSplitGraph}\left(P\,\mathrm{decomposition}\right)$

$\mathrm{true},\left[\left[2\,3\right]\,\left[1\,4\right]\right]$

$G≔\mathrm{SpecialGraphs}:-\mathrm{PetersenGraph}\left(\right)$

$G≔\mathrm{Graph\; 3:\; an\; undirected\; unweighted\; graph\; with\; 10\; vertices\; and\; 15\; edge(s)}$

$\mathrm{IsSplitGraph}\left(G\right)$

$\mathrm{false}$

The GraphTheory[IsSplitGraph] command was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.