Robertson–Wegner graph

Robertson–Wegner graph
Named after	Neil Robertson
Vertices	30
Edges	75
Radius	3
Diameter	3
Girth	5
Automorphisms	20
Chromatic number	4
Chromatic index	5[1]
Properties	Cage

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 G. Wegner.^[2][3][4]

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

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

References

1. Weisstein, Eric W. "Class 2 Graph". MathWorld.
2. Weisstein, Eric W. "Robertson–Wegner Graph". MathWorld.
3. Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 238, 1976.
4. Wong, P. K. "A note on a paper of G. Wegner", J. of Combinatorial Theory, Series B, 22:3, June 1977, pgs 302-303, doi:10.1016/0095-8956(77)90081-8