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Robertson-Wegner Graph

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Robertson-WegnerGraph

The Robertson-Wegner graph is of the four (5,5)-cage graphs, also called Robertson's cage (Read and Wilson 1998, p. 273). Like the other (5,5)-cages, the Robertson-Wegner graph has 30 nodes. It has 75 edges, girth 5, diameter 3, and chromatic number 4. The Robertson-Wegner graph has automorphism group order 20.

The Robertson-Wegner graph is implemented in the Wolfram Language as GraphData["RobertsonWegnerGraph"].

Note that the graph depicted in Bondy and Murty (1976, p. 238) and labeled "(5,5)-cage: The Robertson-Wegner graph" is actually a different (5,5)-cage, namely the Wong graph.

It has LCF notation signature 5^21^(9655366) and is illustrated above in its two order-5 LCF embeddings.

See also

Cage Graph, Foster Cage, Meringer Graph, Robertson Graph, Wong Graph

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References

Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 238, 1976.House of Graphs. "Robertson Wegner Graph." https://houseofgraphs.org/graphs/1290.Meringer, M. "Fast Generation of Regular Graphs and Construction of Cages." J. Graph Th. 30, 137-146, 1999.Read, R. C. and Wilson, R. J. An Atlas of Graphs. Oxford, England: Oxford University Press, p. 273, 1998.Wegner, G. "A Smallest Graph of Girth 5 and Valency 5." J. Combin. Th. B 14, 203-208, 1973.

Referenced on Wolfram|Alpha

Robertson-Wegner Graph

Cite this as:

Weisstein, Eric W. "Robertson-Wegner Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Robertson-WegnerGraph.html

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