The Robertson graph is the unique -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.
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).
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.
-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.
