| 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 K3,3 for each ≥ 1 whose fibre‐preserving automorphism subgroups act arc‐transitively. As a result, a new infinite family of cubic 1‐regular graphs is constructed. © 2003 Wiley Periodicals, Inc. J Graph Theory 45: 101–112, 2004 |
