Arc-transitive Z_p-regular Coverings Of K₄,₄

A undirected regular graphΓis called arc-transitive or symmetric, if it has no isolated vertices and its full automorphism group Aut(Γ) acts transitively on its arc set. p is a projection fromΓtoΓ, A coveringΓofΓwith a projection p is said to be regular (or K-covering) if there is a semiregular subgroup K of the automorphism group Aut(Γ) such that graphΓis isomorphic to the quotient graphΓ/K, say by h,and the quotient mapΓ→Γ/K is the composition ph of p and h. In this paper,we investigate the arc-transitive Zp-regular coverings of K4,4(p> 23), and obtain a new infinite families of 4-valent one-regular graphs as the covering graphs of K4,4 by Zp.