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

  • Authors:

  • Jin-Xin Zhou;Yan-Quan Feng

  • Affiliations:

  • -;-

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

Abstract

A regular cover X@? of 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.