The LeviGraph() command returns the Levi graph, also known as the Tutte-Coxeter graph or the Tutte 8-cage graph. It is a 3-regular graph with 30 vertices and 45 edges.

It is bipartite and is the smallest cubic graph of girth 8.

The Tutte8CageGraph() command is an alias for LeviGraph().

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

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

$G≔\mathrm{Tutte8CageGraph}\left(\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 30\; vertices\; and\; 45\; edge(s)}$

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

$\mathrm{true}$

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

"Tutte-Coxeter graph", Wikipedia. http://en.wikipedia.org/wiki/Tutte-Coxeter_graph

Tutte, William Thomas. (1947). "A family of cubical graphs". Proc. Cambridge Philos. Soc. 43 (04): 459–474. doi:10.1017/S0305004100023720.