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. Moore graphs were named by Hoffman & Singleton (1960) 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 (Erdõs, Rényi & Sós 1966). 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.

Read more about Moore GraphBounding Vertices By Degree and Diameter, Moore Graphs As Cages, Examples

Other articles related to "moore graph, moore graphs, graphs, graph":

Moore Graph - Examples
... The Hoffman–Singleton theorem states that any Moore graph with girth 5 must have degree 2, 3, 7, or 57 ... The Moore graphs are The complete graphs on n > 2 nodes ... (diameter 2, girth 5, degree 3, order 10) The Hoffman–Singleton graph ...

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