Search for properties of the missing Moore graph

Abstract

In the degree-diameter problem, the only extremal graph the existence of which is still in doubt is the Moore graph of order 3250, degree 57 and diameter 2. It has been known that such a graph cannot be vertex-transitive. Also, certain restrictions on the structure of the automorphism group of such a graph have been known in the case when the order of the group is even. In this paper we further investigate symmetries and structural properties of the missing Moore (57, 2)-graph(s) with the help of a combination of spectral, group-theoretic, combinatorial, and computational methods. One of the consequences is that the order of the automorphism group of such a graph is at most 375. © 2009 Elsevier Inc. All rights reserved.