BrinkmannGraph - Maple Help

GraphTheory[SpecialGraphs]

 BrinkmannGraph
 construct Brinkmann graph

 Calling Sequence BrinkmannGraph()

Description

 • The BrinkmannGraph() command constructs the Brinkmann graph, a 4-regular graph with 21 vertices and 42 edges.
 • The Brinkmann graph was first described by Gunnar Brinkmann.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $C≔\mathrm{BrinkmannGraph}\left(\right)$
 ${C}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 21 vertices and 42 edge\left(s\right)}}$ (1)
 > $\mathrm{ChromaticNumber}\left(C\right)$
 ${4}$ (2)
 > $G≔\mathrm{AutomorphismGroup}\left(C\right)$
 ${G}{≔}⟨\left({2}{,}{3}\right)\left({4}{,}{5}\right)\left({6}{,}{7}\right)\left({8}{,}{12}\right)\left({9}{,}{11}\right)\left({10}{,}{19}\right)\left({13}{,}{15}\right)\left({14}{,}{17}\right)\left({20}{,}{21}\right){,}\left({1}{,}{2}\right)\left({3}{,}{10}\right)\left({5}{,}{8}\right)\left({7}{,}{9}\right)\left({11}{,}{13}\right)\left({12}{,}{14}\right)\left({15}{,}{16}\right)\left({17}{,}{18}\right)\left({19}{,}{20}\right)⟩$ (3)
 > $\mathrm{GroupTheory}:-\mathrm{GroupOrder}\left(G\right)$
 ${14}$ (4)
 > $\mathrm{DrawGraph}\left(C\right)$

References

 "Brinkmann graph", Wikipedia. http://en.wikipedia.org/wiki/Brinkmann_graph
 Brinkmann G., Meringer M. "The Smallest 4-Regular 4-Chromatic Graphs with Girth 5." Graph Theory Notes of New York 32, 40-41, 1997.

Compatibility

 • The GraphTheory[SpecialGraphs][BrinkmannGraph] command was introduced in Maple 2019.