Robertson–Wegner graph

Template:Short description Template:Infobox graph In the mathematical field of graph theory, the Robertson–Wegner graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Neil Robertson and Gerd Wegner.^[1]^[2]^[3]

It is one of the four (5,5)-cage graphs, the others being the Foster cage, the Meringer graph, and the Wong graph.

It has chromatic number 4, diameter 3, and is 5-vertex-connected.

Algebraic properties

The characteristic polynomial of the Robertson–Wegner graph is

(x - 5) (x - 2)^{8} (x + 1) (x + 3)^{4} (x^{4} + 2 x^{3} - 4 x^{2} - 5 x + 5)^{2} (x^{4} + 2 x^{3} - 6 x^{2} - 7 x + 11)^{2} .

↑ Template:MathWorld
↑ Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 238, 1976.
↑ Wong, P. K. "A note on a paper of G. Wegner", Journal of Combinatorial Theory, Series B, 22:3, June 1977, pgs 302-303, doi:10.1016/0095-8956(77)90081-8