Meringer graph

Meringer graph
Named after	Markus Meringer
Vertices	30
Edges	75
Radius	3
Diameter	3
Girth	5
Automorphisms	96
Chromatic number	3
Chromatic index	5
Properties	Cage

In the mathematical field of graph theory, the Meringer graph is a 5-regular undirected graph with 30 vertices and 75 edges named after Markus Meringer.^[1][2]

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

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

Algebraic properties

The characteristic polynomial of the Meringer graph is

$(x-5) (x-2)^9 x (x+2)^3 (x+3)^2 (x^2+x-4)^3 (x^2+2x-2)^4.$

References

1. Weisstein, Eric W., "Meringer Graph", MathWorld.
2. Meringer, Markus (1999), "Fast generation of regular graphs and construction of cages", Journal of Graph Theory 30 (2): 137–146, doi:10.1002/(SICI)1097-0118(199902)30:2<137::AID-JGT7>3.0.CO;2-G, MR 1665972.