parameters : keyword option of the form parameters=true or parameters=false. This specifies whether the parameters [k, lambda, mu] should be returned when the graph is strongly regular. The default is false.

The IsStronglyRegular(G) command returns true if G is a strongly regular graph and false otherwise.

An undirected graph G is strongly regular if there exist integers k, lambda, and mu such that every vertex has k neighbors and for every pair of vertices (u,v), u and v have exactly lambda neighbors in common if they are themselves adjacent, and exactly mu neighbors in common if they are not.

Note that some parts of this definition may be satisfied trivially, in which a complete graph every pair of vertices is adjacent, so the choice of mu could be arbitrary and therefore mu is undefined.

Any strongly regular graph is regular, but the converse is not true.

The following are graphs in the SpecialGraphs subpackage which are strongly regular.

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

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

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

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 4\; vertices\; and\; 4\; edge(s)}$

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

$\left[2\,2\,3\,1\right]$

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

$\mathrm{false}$

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

$P≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 10\; vertices\; and\; 15\; edge(s)}$

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

$\left[3\,3\,3\,3\,3\,3\,3\,3\,3\,3\right]$

$\mathrm{IsStronglyRegular}\left(P\,'\mathrm{parameters}'\right)$

$\mathrm{true},\left[3\,0\,1\right]$

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

$C≔\mathrm{ClebschGraph}\left(\right)$

$C≔\mathrm{Graph\; 3:\; an\; undirected\; graph\; with\; 16\; vertices\; and\; 40\; edge(s)}$

$\mathrm{IsStronglyRegular}\left(C\,'\mathrm{parameters}'\right)$

$\mathrm{true},\left[5\,0\,2\right]$

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

The GraphTheory[IsStronglyRegular] command was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.