The GearGraph(n) function creates the gear graph on 2n+1 vertices.

The gear graph, also called the bipartite wheel graph, can be seen as a wheel graph in which a vertex has been inserted between each vertex other than the central vertex.

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

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

$G≔\mathrm{GearGraph}\left(5\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 11\; vertices\; and\; 15\; edge(s)}$

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

$\left\{\left\{0\,2\right\}\,\left\{0\,4\right\}\,\left\{0\,6\right\}\,\left\{0\,8\right\}\,\left\{0\,10\right\}\,\left\{1\,2\right\}\,\left\{1\,10\right\}\,\left\{2\,3\right\}\,\left\{3\,4\right\}\,\left\{4\,5\right\}\,\left\{5\,6\right\}\,\left\{6\,7\right\}\,\left\{7\,8\right\}\,\left\{8\,9\right\}\,\left\{9\,10\right\}\right\}$

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

The GraphTheory[SpecialGraphs][GearGraph] command was introduced in Maple 2018.

For more information on Maple 2018 changes, see Updates in Maple 2018.