Journal of Guangxi Normal University(Natural Science Edition) ›› 2014, Vol. 32 ›› Issue (4): 66-71.

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1-Regular Cayley Graphs of Valency 9 with Elementary Abelian Vertex Stabilizer

XU Shang-Jin1,2, QIN Yan-li1,2, ZHANG Yue-feng1,2, LI Jing-jian1,2   

  1. 1.College of Mathematices and Information Sciences, Guangxi University,Nanning Guangxi 530004, China;
    2.Guangxi Colleges and Universities Key Laboratory of Mathematics and Its Applications, Nanning Guangxi 530004, China
  • Received:2014-07-16 Published:2018-09-26

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Abstract: A graph Γ is called 1-regular if its full automorphism group Aut (Γ) acts regularly on its arcs. In this paper, a complete classifcation for 1-regular Cayley graphs of valency 9 with the vertex stabilizer being elementary abelian is presented. It is proved that there exists only one core-free 1-regular Cayley graphs of valency 9 with an elementary abelian vertex stabilizer.

Key words: 1-regular, Cayley graph, core-free

CLC Number: 

  • O157
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