S-REGULAR CUBIC GRAPHS AS COVERINGS OF THE COMPLETE BIPARTITE GRAPH K-3,K-3

Abstract

A graph is s-regular if its automorphism group acts freely and transitively on the set of s-arcs. An infinite family of cubic 1-regular graphs was constructed in [10], as cyclic coverings of the three-dimensional Hypercube. In this paper, we classify the s-regular cyclic coverings of the complete bipartite graph k(3,3) for each s greater than or equal to 1 whose fibre-preserving automorphism subgroups act arc-transitively. As a result, a new infinite family of cubic 1-regular graphs is constructed. (C) 2003 Wiley Periodicals, Inc. J Graph Theory 45: 101-112, 2004.