Robertson–Wegner 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.^[2][3][4]

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
Table of graphs and parameters

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

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