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Arc-transitive cubic graphs of order four times an odd square-free integer

Bo Ling

School of Mathematics and Computer Sciences, Yunnan Minzu University, Kunming, Yunnan 650031, P. R. China

E-mail Address: bolinggxu@163.com

Corresponding author.

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and

Ben Gong Lou

School of Mathematics and Statistics, Yunnan University, Kunmin 650031, P. R. China

E-mail Address: bengong188@163.com

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https://doi.org/10.1142/S0219498817502139Cited by:4 (Source: Crossref)

Abstract

Xu, Zhang and Zhou [Chin. Ann. Math.25B(4) (2004) 545–554] classified all arc-transitive cubic graphs of order $4 p$ with $p$ a prime. In this paper, we shall generalize this result by classifying all connected arc-transitive cubic graphs of order four times an odd square-free integer. It is shown that, for each of such graphs $Γ$ , either the full automorphism group $A u t Γ$ is isomorphic to $P S L (2, p)$ , $P G L (2, p)$ , $P S L (2, p) \times ℤ_{2}$ or $P G L (2, p) \times ℤ_{2}$ , or $Γ$ is isomorphic to one of 5 graphs.

Communicated by D. S. Passman

Keywords:

AMSC: 05C25, 05E18, 20B25

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