FosterCageGraph - Maple Help
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GraphTheory[SpecialGraphs]

 FosterCageGraph
 construct Foster cage graph
 MeringerGraph
 construct Meringer graph
 RobertsonWegnerGraph
 construct Robertson-Wegner graph
 WongGraph
 construct Wong graph

 Calling Sequence FosterCageGraph() MeringerGraph() RobertsonWegnerGraph() WongGraph()

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $G≔\mathrm{MeringerGraph}\left(\right)$
 ${G}{≔}{\mathrm{Graph 1: an undirected graph with 30 vertices and 75 edge\left(s\right)}}$ (1)
 > $\mathrm{DrawGraph}\left(G\right)$

References

 "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.