2-Arc-transitive cyclic covers of K n,n −nK 2

Abstract

Du et al. (in J. Comb. Theory B 74:276---290, 1998 and J. Comb. Theory B 93:73---93, 2005), classified regular covers of complete graph whose fiber-preserving automorphism group acts 2-arc-transitively, and whose covering transformation group is either cyclic or isomorphic to $\mathbb{Z}_{p}^{2}$ or $\mathbb{Z}_{p}^{3}$ with p a prime. In this paper, a complete classification is achieved of all the regular covers of bipartite complete graphs minus a matching K n,n ?nK 2 with cyclic covering transformation groups, whose fiber-preserving automorphism groups act 2-arc-transitively.