The FosterCageGraph(), MeringerGraph(), RobertsonWegnerGraph(), and WongGraph() commands return the Foster cage graph, the Meringer graph, the Robertson-Wegner graph, and the Wong graph respectively.

These four graphs are all undirected graphs with 30 vertices, 75 edges, diameter 3, and girth 5.

Together these graphs comprise the complete list of known (5,5) cage graphs.

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

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

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

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 30\; vertices\; and\; 75\; edge(s)}$

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

"Foster cage", Wikipedia. http://en.wikipedia.org/wiki/Foster_cage

"Meringer graph", Wikipedia. http://en.wikipedia.org/wiki/Meringer_graph

"Robertson-Wegner graph", Wikipedia. http://en.wikipedia.org/wiki/Robertson-Wegner_graph

"Wong graph", Wikipedia. http://en.wikipedia.org/wiki/Wong_graph

Meringer, M. "Fast Generation of Regular Graphs and Construction of Cages." J. Graph Th. 30, 137-146, 1999.

Wegner, G. "A Smallest Graph of Girth 5 and Valency 5." J. Combin. Th. B 14, 203-208, 1973.