2-Arc-transitive metacyclic covers of complete graphs

Abstract

Regular covers of complete graphs whose fibre-preserving automorphism groups act 2-arc-transitively are investigated. Such covers have been classified when the covering transformation groups K are cyclic groups Z(d) for an integer d >= 2, metacyclic abelian groups Z(p)(2), or nonmetacyclic abelian groups Z(p)(3) for a prime p (see S.F. Du et al. (1998) [5] for the first two metacyclic group cases and see S.F. Du et al. (2005) [3] for the third nonmetacyclic group case). In this paper, a complete classification is achieved of all such covers when K is any metacyclic group. (C) 2014 Elsevier Inc. All rights reserved.116Ysciescopu