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2-ARC-TRANSITIVE REGULAR COVERS OF $K_{n,n}-nK_{2}$ HAVING THE COVERING TRANSFORMATION GROUP $\mathbb{Z}_{p}^{3}$

  • SHAOFEI DU (a1) and WENQIN XU (a2)

Abstract

This paper contributes to the regular covers of a complete bipartite graph minus a matching, denoted $K_{n,n}-nK_{2}$ , whose fiber-preserving automorphism group acts 2-arc-transitively. All such covers, when the covering transformation group $K$ is either cyclic or $\mathbb{Z}_{p}^{2}$ with $p$ a prime, have been determined in Xu and Du [‘2-arc-transitive cyclic covers of $K_{n,n}-nK_{2}$ ’, J. Algebraic Combin. 39 (2014), 883–902] and Xu et al. [‘2-arc-transitive regular covers of $K_{n,n}-nK_{2}$ with the covering transformation group $\mathbb{Z}_{p}^{2}$ ’, Ars. Math. Contemp. 10 (2016), 269–280]. Finally, this paper gives a classification of all such covers for $K\cong \mathbb{Z}_{p}^{3}$ with $p$ a prime.

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2-ARC-TRANSITIVE REGULAR COVERS OF $K_{n,n}-nK_{2}$ HAVING THE COVERING TRANSFORMATION GROUP $\mathbb{Z}_{p}^{3}$

  • SHAOFEI DU (a1) and WENQIN XU (a2)

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