Moore Graphs and Cycles Are Extremal Graphs for Convex Cycles
Jernej Azarija, Sandi Klavžar · Journal of Graph Theory · 2014
Abstract Let denote the number of convex cycles of a simple graph G of order n , size m , and girth . It is proved that and that equality holds if and only if G is an even cycle or a Moore graph. The equality also holds for a possible Moore graph of diameter 2 and degree 57 thus giving a new characterization of Moore graphs.