Arc-transitive cyclic and dihedral covers of pentavalent symmetric graphs of order twice a prime

Yan-Quan Feng, Da-Wei Yang, Jin-Xin Zhou

Abstract


A regular cover of a connected graph is called cyclic or dihedral if its transformation group is cyclic or dihedral respectively, and arc-transitive (or symmetric) if the fibre-preserving automorphism subgroup acts arc-transitively on the regular cover. In this paper, we give a classification of arc-transitive cyclic and dihedral covers of a connected pentavalent symmetric graph of order twice a prime. All those covers are explicitly constructed as Cayley graphs on some groups, and their full automorphism groups are determined.


Keywords


Symmetric graph, Cayley graph, bi-Cayley graph, regular cover

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DOI: https://doi.org/10.26493/1855-3974.1409.e54

ISSN: 1855-3974

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