Journal of Guangxi Normal University(Natural Science Edition) ›› 2015, Vol. 33 ›› Issue (1): 59-66.doi: 10.16088/j.issn.1001-6600.2015.01.010

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8-Valent 1-Regular Cayley Graphs WhoseVertex Stabilizer is Z4×Z2

XU Shang-Jin1,2, LI Ping-shan1,2, HUANG Hai-hua1,2, 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 Online:2015-03-15 Published:2018-09-17

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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 characterization for 8-valent 1-regular Cayley Graphs with point stabilizer is presented. It is proved that there exists only 2 core-free 8-valent 1-regular Cayley graphs whose point stabilizer is Z4×Z2.

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

CLC Number: 

  • O157
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