An undirected graph G is regular if each vertex has the same degree. For example, CycleGraph(4) is a regular graph of degree 2.

The IsRegular command returns true if the graph is regular and false otherwise. If a name d is specified, then this name is assigned the degree of the graph. If the graph is not regular and a name is specified, then the name is assigned FAIL.

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

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

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

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 4\; vertices\; and\; 4\; edges}$

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

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

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

$\mathrm{false}$

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

$P≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 10\; vertices\; and\; 15\; edges}$

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

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

$\mathrm{IsRegular}\left(P\,'r'\right)$

$\mathrm{true}$

$r$

$3$

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

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

$C≔\mathrm{Graph\; 3:\; an\; undirected\; graph\; with\; 16\; vertices\; and\; 40\; edges}$

$\mathrm{IsRegular}\left(C\,'r'\right)$

$\mathrm{true}$

$r$

$5$

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