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Robertson Graph

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RobertsonGraph

The Robertson graph is the unique (4,5)-cage graph, illustrated above. It has 19 vertices and 38 edges. It has girth 5, diameter 3, chromatic number 3, and is a quartic graph.

It is implemented in the Wolfram Language as GraphData["RobertsonGraph"].

The Robertson graph has automorphism group order 24, possesses 5376 (directed) Hamiltonian cycles, and has 224 distinct order-1 generalized LCF notations (with none of higher order).

See also

Cage Graph, Robertson's Apex Graph, Robertson-Wegner Graph

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References

Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 237, 1976.Exoo, G. "Rectilinear Drawings of Famous Graphs: The (4,5)-Cage." http://isu.indstate.edu/ge/COMBIN/RECTILINEAR/cage45.gif.Robertson, N. "The Smallest Graph of Girth 5 and Valency 4." Bull. Amer. Math. Soc. 70, 824-825, 1964.Wong, P. K. "Cages--A Survey." J. Graph Th. 6, 1-22, 1982.

Referenced on Wolfram|Alpha

Robertson Graph

Cite this as:

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

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