The DeBruijnGraph() command returns the De Bruijn graph, a directed graph whose vertices are sequences of symbols of length n chosen from some alphabet of size m whose edges indicate the sequences which may overlap.

The graph has $m^n$ vertices, each of which corresponds to a sequence of the $m$ symbols of length $n$.  It is named for Nicolaas Govert de Bruijn.

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

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

$\mathrm{G32}≔\mathrm{DeBruijnGraph}\left(3\,2\right)$

$\mathrm{G32}≔\mathrm{Graph\; 1:\; a\; directed\; unweighted\; graph\; with\; 9\; vertices,\; 24\; arc(s),\; and\; 3\; self-loop(s)}$

$\mathrm{DrawGraph}\left(\mathrm{G32}\right)$

$\mathrm{G53}≔\mathrm{DeBruijnGraph}\left(5\,3\right)$

$\mathrm{`Graph\; 2:\; a\; directed\; unweighted\; graph\; with\; 125\; vertices,\; 620\; arc(s),\; and\; 5\; self-loop(s)`}$

$\mathrm{Graph\; 2:\; a\; directed\; unweighted\; graph\; with\; 125\; vertices,\; 620\; arc(s),\; and\; 5\; self-loop(s)}$

$\mathrm{NumberOfSelfLoops}\left(\mathrm{G53}\right)$

$5$

$\mathrm{NumberOfEdges}\left(\mathrm{G53}\right)$

$625$

$\mathrm{IsEulerian}\left(\mathrm{G53}\right)$

$\mathrm{true}$

The GraphTheory[SpecialGraphs][DeBruijnGraph] command was introduced in Maple 2020.

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