The TutteGraph() command returns the Tutte graph, a 3-regular graph with 46 vertices and 69 edges, named after W. T. Tutte.

It is a cubic polyhedral graph, but is non-hamiltonian. It was published by Tutte as a counterexample to a conjecture by P. G. Tait that every 3-regular polygon is Hamiltonian.

The Tutte graph should not be confused with the Tutte 8-cage or Tutte 12-cage graphs.

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

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

$G≔\mathrm{TutteGraph}\left(\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 46\; vertices\; and\; 69\; edges}$

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

$3$

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

"Tutte graph", Wikipedia. http://en.wikipedia.org/wiki/Tutte_graph

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

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