On cyclic regular covers of complete graphs of small order

Pan, Jiangmin; Huang, Zhaohong; Xu, Fenghui; Ding, Suyun

doi:10.1016/j.disc.2014.04.023

Cited by 4 publications

(3 citation statements)

References 24 publications

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“…Based on the approaches studied in [12,26], many arc-transitive covers of symmetric graphs of small orders and small valencies have been classified. For example, Pan et al [29] studied arc-transitive cyclic covers of some complete graphs of small orders. One some notation and preliminary results.…”

Section: Introductionmentioning

confidence: 99%

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

Yan

Yang²,

Zhou³

2018

Ars Math. Contemp.

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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 fibrepreserving 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.

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Section: Introductionmentioning

confidence: 99%

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

Yan

Yang²,

Zhou³

2018

Ars Math. Contemp.

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show abstract

“…Based on the approaches studied in [11,25], many arc-transitive covers of symmetric graphs of small orders and small valencies have been classified. For example, Pan et al [27] studied arctransitive cyclic covers of some complete graphs of small orders. One may see [1,26] for other works.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we consider arc-transitive cyclic and dihedral covers of these graphs. For K 6 , the cyclic covers have been classified in [27], which should be the complete bipartite graph K 6,6 and the Icosahedron graph I 12 (note that I 12 is missed in [27]). For CD p , the cyclic covers consist of six infinite families of graphs, which are Cayley graphs on generalized dihedral groups.…”

Section: Introductionmentioning

confidence: 99%

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

Yang¹,

Yan²,

Zhou³

2017

Preprint

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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.

show abstract