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

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, MR 1665972, doi:10.1002/(SICI)1097-0118(199902)30:2<137::AID-JGT7>3.0.CO;2-G.
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