Cubic Cayley graphs with small diameter.

Abstract

In this paper we apply Polya's Theorem to the problem of enumerating Cayley graphs on permutation groups up to isomorphisms induced by conjugacy in the symmetric group. We report the results of a search of all three-regular Cayley graphs on permutation groups of degree at most nine for small diameter graphs. We explore several methods of constructing covering graphs of these Cayley graphs. Examples of large graphs with small diameter are obtained.

Keywords

• permutation group
• cayley graph
• cubic graph
• diameter
• polya's theorem
• permutation group.
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]