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
	Table of graphs and parameters

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

Weisstein, Eric W. "Meringer Graph". MathWorld.
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.

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[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.