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

Part of: Algebraic combinatorics Permutation groups Graph theory

Published online by Cambridge University Press:  16 March 2016

SHAOFEI DU  and
WENQIN XU
SHAOFEI DU*
Affiliation:
School of Mathematical Sciences, Capital Normal University, Beijing 100048, PR China email dushf@cnu.edu.cn
WENQIN XU
Affiliation:
School of Mathematical Sciences, Capital Normal University, Beijing 100048, PR China email wenqinxu85@163.com
*
✉dushf@cnu.edu.cn
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Abstract

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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.

Keywords

arc-transitive graphcovering graphlifting2-transitive group

MSC classification

Primary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Secondary: 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures 05E30: Association schemes, strongly regular graphs
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 101 , Issue 2 , October 2016 , pp. 145 - 170
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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