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.

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

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

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

$C≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 21\; vertices\; and\; 42\; edge(s)}$

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

$4$

$G≔\mathrm{AutomorphismGroup}\left(C\right)$

$G≔⟨\left(1\,2\right)\left(3\,10\right)\left(5\,8\right)\left(7\,9\right)\left(11\,13\right)\left(12\,14\right)\left(15\,16\right)\left(17\,18\right)\left(19\,20\right)\,\left(2\,3\right)\left(4\,5\right)\left(6\,7\right)\left(8\,12\right)\left(9\,11\right)\left(10\,19\right)\left(13\,15\right)\left(14\,17\right)\left(20\,21\right)⟩$

$\mathrm{GroupTheory}:-\mathrm{GroupOrder}\left(G\right)$

$14$

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

"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.

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

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