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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

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

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


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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