Geodesic
Arc-transitive cyclic and dihedral covers of pentavalent symmetric graphs of order twice a prime
Ars Mathematica Contemporanea, Tome 15 (2018) no. 2, pp. 499-522.

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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.
DOI : 10.26493/1855-3974.1409.e54
Keywords: Symmetric graph, Cayley graph, bi-Cayley graph, regular cover 
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Yan-Quan Feng; Da-Wei Yang; Jin-Xin Zhou. Arc-transitive cyclic and dihedral covers of pentavalent symmetric graphs of order twice a prime. Ars Mathematica Contemporanea, Tome 15 (2018) no. 2, pp. 499-522. doi : 10.26493/1855-3974.1409.e54. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1409.e54/

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