Moore graph

In graph theory, a Moore graph is a regular graph of degree d and diameter k whose number of vertices equals the upper bound

An equivalent definition of a Moore graph is that it is a graph of diameter k with girth 2k + 1. Another equivalent definition of a Moore graph G is that it has girth g = 2k+1 and precisely cycles of length g, where n,m is the number of vertices (resp. edges) of G. They are in fact extremal with respect to the number of cycles whose length is the girth of the graph (Azarija & Klavžar 2015).