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.

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


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