In this paper, a complete classification is achieved of all the regular covers of the complete bipartite graphs Kn,n with cyclic covering transformation group, whose fibre-preserving automorphism group acts 2-arc-transitively. All these covers consist of one threefold covers of K6,6, one twofold cover of K12,12 and one infinite family X(r, p) of p-fold covers of Kpr,pr with p a prime and r an integer such that pr ≥ 3. This infinite family X(r, p) can be derived by a very simple and nice voltage assignment f as follows: X(r, p) = Kpr,pr × f Zp, where Kpr,pr is a complete bipartite graph with the bipartition V = {α α ∈ V(r, p)}∪{α α ∈ V(r, p)} for the r-dimensional vector space V(r, p) over the field of order p and fα,β  = r i=1 aibi, for all α = (ai)r, β = (bi)r ∈ V(r, p).

EB00000003568K

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