The Description Of Arc-transitive Zp-regular Coverings Of K4,4

A graphГis called a G-symmetric graph, ifГhas no isolated vertices and G acts transitively on the arc set ofГ, for G≤Aut(Г). In particular,we callГa symmetric graph if G=Aut(Г). p is a projection fromГtoГ,a coveringГofГwith a projection p is said to be regular covering(orK-covering) if there is a semiregular subgroup K of the automorphism group AutГsuch that graphГis isomorphic to the quotient graphГ/K,say by h,and the quotient mapГ→Г/K is the composition ph of p and h. In this paper, we discuss the arc-transitive Zp-regular coverings of K4,4,and classify all of arc-transitive Zp-regular coverings of K4,4.As a result, a new infinite family of symmetric graphs as the covering graphs K4,4 by Zp are constructed.