Edge-transitive cyclic regular covers of the Mobius-Kantor graph

A regular cover (X) over tilde a connected graph X is called elementary abelian or cyclic if its group of covering transformations is elementary abelian or cyclic, respectively. Elementary abelian regular covers of the Mobius-Kantor graph whose fiber preserving groups are edge- but not vertex-transitive were considered by Malnic et al. [A. Malnic, D. Marusic, S. Miklavic, P. Potocnik, Semisymmetric elementary abelian covers of the Mobius-Kantor graph, Discrete Math. 307 (2007) 2156-2175]. In this paper, cyclic regular covers of the Mobius-Kantor graph whose fiber-preserving groups are edge-transitive are classified. As an application, cubic edge-transitive graphs of order 16p for each prime p are classified. Also, it is shown that with the exception of the Ljubljana graph on 112 vertices, all cubic edge-transitive graphs of order 16p are arc-transitive. (C) 2011 Elsevier Ltd. All rights reserved.