Nonexistence of an extremal graph of a certain type

Abstract

Cubic Moore graphs of diameter k on 3.2k — 2 vertices do not exist for k > 2. This paper exhibits the first known case of nonexistence for generalized cubic Moore graphs when the number of vertices is just less than the critical number for a Moore graph : the generalized Moore graph on 44 vertices does not exist. © 1980, Australian Mathematical Society. All rights reserved.