The Meringer graph is one of the four 
-cage graphs, discovered
by Meringer (1999) after it had long been thought that only three such cages existed.
Like the other 
-cages,
the Meringer graph has 30 nodes. It has 75 edges, girth 5, diameter 3, chromatic
number 3, and is a quintic graph. The order
of its automorphism group is 96. It is illustrated
above in a number of degree-3 LCF notations, of which
at least 108 distinct of which exist.
The plots above show the adjacency, incidence, and distance matrices of the graph.
The graph spectrum of the Meringer graph is 
.
