Moore Graph (Paperback)

High Quality Content by WIKIPEDIA articles! 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. Moore graphs were named by Hoffman & Singleton after Edward F. Moore, who posed the question of describing and classifying these graphs. As well as having the maximum possible number of vertices for a given combination of degree and diameter, Moore graphs have the minimum possible number of vertices for a regular graph with given degree and girth. That is, any Moore graph is a cage. The formula for the number of vertices in a Moore graph can be generalized to allow a definition of Moore graphs with even girth as well as odd girth, and again these graphs are cages.