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On tetravalent $s$ -regular Cayley graphs

Jing Jian Li

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

School of Mathematics and Information Sciences, Guangxi University, Nanning 530004, P. R. China

Guangxi Colleges and Universities Key Laboratory of Mathematics and Its Applications, Nanning, P. R. China

E-mail Address: lijjhx@163.com

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Bo Ling

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

E-mail Address: bolinggxu@163.com

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Jicheng Ma

Chongqing Key Laboratory of Group & Graph Theories and Applications, Chongqing University of Arts and Sciences, Chongqing 402160, P. R. China

E-mail Address: ma_jicheng@hotmail.com

Corresponding author.

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https://doi.org/10.1142/S021949881750195XCited by:4 (Source: Crossref)

Abstract

A Cayley graph $Γ = C a y (G, S)$ is said to be core-free if $G$ is core-free in some $X$ for $G \leq X \leq A u t Γ$ . A graph $Γ$ is called $s$ -regular if $A u t Γ$ acts regularly on its $s$ -arcs. It is shown in this paper that if $s \leq 2$ , then there exist no core-free tetravalent $s$ -regular Cayley graphs; and for $s \geq 3$ , every tetravalent $s$ -regular Cayley graph is a normal cover of one of the three known core-free graphs. In particular, a characterization of tetravalent $s$ -regular Cayley graphs is given.

Communicated by X.-D. Hou

Keywords:

AMSC: 20B25, 05C25, 05E18

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