2-Arc-Transitive regular covers of K_{n,n} - nK_2 with the covering transformation group Z_p^2

Wenqin Xu, Yanhong Zhu, Shaofei Du

Abstract


In 2014, Xu and Du classified all regular covers of a complete bipartite graph Kn, n minus a matching, denoted by Kn, n − nK2, whose covering transformation group is cyclic and whose fibre-preserving automorphism group acts 2-arc-transitively. In this paper, a further classification is achieved for all the regular covers of Kn, n − nK2, whose covering transformation group is isomorphic to Zp2 with p a prime and whose fibre-preserving automorphism group acts 2-arc-transitively. Actually, there are only few covers with these properties and it is shown that all of them are covers of K4, 4 − 4K2.


Keywords


Arc-transitive graph, covering graph, 2-transitive group

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DOI: https://doi.org/10.26493/1855-3974.560.5be

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications