Meringer graph

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]

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

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

${\displaystyle (x-5)(x-2)^{9}x(x+2)^{3}(x+3)^{2}(x^{2}+x-4)^{3}(x^{2}+2x-2)^{4}.}$