Edge-transitive regular Z(n)-covers of the Heawood graph

摘要

A regular cover of a graph is said to be an edge-transitive cover if the fibre-preserving automorphism subgroup acts edge-transitively on the covering graph. In this paper we classify edge-transitive regular Z(n)-covers of the Heawood graph, and obtain a new infinite family of one-regular cubic graphs. Also, as an application of the classification of edge-transitive regular Z(n)-covers of the Heawood graph, we prove that any bipartite edge-transitive cubic graph of order 14p is isomorphic to a normal Cayley graph of dihedral group if the prime p > 13.