The CrownGraph(n) function creates the crown graph on 2n vertices.

The crown graph is a bipartite graph with vertices $\left[u_1\,\mathrm{...}\,u_n\,v_1\,\mathrm{...}\,v_n\right]$ in which an edge exists between $\left[u_i\right]$ and $v_j$ whenever i differs from j.

A crown graph with 2n vertices has $n\left(n-1\right)$ edges.

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

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

$G≔\mathrm{CrownGraph}\left(5\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 10\; vertices\; and\; 20\; edge(s)}$

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

$\left\{\left\{1\,4\right\}\,\left\{1\,6\right\}\,\left\{1\,8\right\}\,\left\{1\,10\right\}\,\left\{2\,3\right\}\,\left\{2\,5\right\}\,\left\{2\,7\right\}\,\left\{2\,9\right\}\,\left\{3\,6\right\}\,\left\{3\,8\right\}\,\left\{3\,10\right\}\,\left\{4\,5\right\}\,\left\{4\,7\right\}\,\left\{4\,9\right\}\,\left\{5\,8\right\}\,\left\{5\,10\right\}\,\left\{6\,7\right\}\,\left\{6\,9\right\}\,\left\{7\,10\right\}\,\left\{8\,9\right\}\right\}$

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

The GraphTheory[SpecialGraphs][CrownGraph] command was introduced in Maple 2021.

For more information on Maple 2021 changes, see Updates in Maple 2021.