Robertson–Wegner graph - Alchetron, The Free Social Encyclopedia

Named after Neil Robertson Edges 75 Diameter 3		Vertices 30 Radius 3 Girth 5

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.

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 .

References

Robertson–Wegner graph Wikipedia

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