Meringer graph

Template:Short description Template:Context Template:Infobox 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.

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

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