The second author et al. [J. Comb. Theory, Ser. B 74, No. 2, 276--290 (1998; Zbl 1026.05057); ibid. 93, No. 1, 73--93 (2005; Zbl 1063.05066)], classified regular covers of complete graph whose fiber-preserving automorphism group acts 2-arc-transitively, and whose covering transformation group is either cyclic or isomorphic to $\mathbb Z_p^2$ or $\mathbb{Z}_p^3$ with $p$ a prime. In this paper, a complete classification is achieved of all the regular covers of bipartite complete graphs minus a matching $K_{n,n}-nK_2$ with cyclic covering transformation groups, whose fiber-preserving automorphism groups act 2-arc-transitively.

05C60, 05C25

arc-transitive graph, covering graph, lifting, 2-transitive group, linear group