GraphTheory[SpecialGraphs] - Maple Programming Help

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GraphTheory[SpecialGraphs]

 DeBruijnGraph
 construct De Bruijn graph

 Calling Sequence DeBruijnGraph(m,n)

Parameters

 m - positive integer n - positive integer

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $\mathrm{G32}≔\mathrm{DeBruijnGraph}\left(3,2\right)$
 ${\mathrm{G32}}{≔}{\mathrm{Graph 1: a directed unweighted graph with 9 vertices, 24 arc\left(s\right), and 3 self-loop\left(s\right)}}$ (1)
 > $\mathrm{DrawGraph}\left(\mathrm{G32}\right)$
 > $\mathrm{G53}≔\mathrm{DeBruijnGraph}\left(5,3\right)$
 > $\mathrm{Graph 2: a directed unweighted graph with 125 vertices, 620 arc\left(s\right), and 5 self-loop\left(s\right)}$
 ${\mathrm{Graph 2: a directed unweighted graph with 125 vertices, 620 arc\left(s\right), and 5 self-loop\left(s\right)}}$ (2)
 > $\mathrm{NumberOfSelfLoops}\left(\mathrm{G53}\right)$
 ${5}$ (3)
 > $\mathrm{NumberOfEdges}\left(\mathrm{G53}\right)$
 ${625}$ (4)
 > $\mathrm{IsEulerian}\left(\mathrm{G53}\right)$
 ${\mathrm{true}}$ (5)

Compatibility

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