Semisymmetric cubic graphs as regular covers of K 3,3

A regular graph X is called semisymmetric if it is edge-transitive but not vertex-transitive. For G . AutX, we call a G-cover X semisymmetric if X is semisymmetric, and call a G-cover X one-regular if AutX acts regularly on its arc-set. In this paper, we give the sufficient and necessary conditions for the existence of one-regular or semisymmetric Z n -covers of K 3,3. Also, an infinite family of semisymmetric Z n . Z n -covers of K 3,3 are constructed.