广西师范大学学报(自然科学版) ›› 2012, Vol. 30 ›› Issue (2): 54-58.

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qp2阶连通4度半传递图

徐尚进1, 张晓均1, 康吉吉2, 李靖建1   

  1. 1.广西大学数学与信息科学学院,广西南宁530004;
    2.武警医学院数理教研室,天津300162
  • 收稿日期:2012-02-09 出版日期:2012-06-20 发布日期:2018-12-03
  • 通讯作者: 徐尚进(1959—),男,安徽庐江人,广西大学教授,博士。E-mail:xusj@gxu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(10961004);广西科学基金资助项目(0832054);广西研究生教育创新计划资助项目(T32575)

Tetravalent Connected Half-transitive Graphs of Order qp2

XU Shang-jin1, ZHANG Xiao-jun1, KANG Zhe2, LI Jing-jian1   

  1. 1.School of Mathematices and Information Sciences,Guangxi University,Nanning Guangxi 530004,China;
    2.Department of Mathematics and Physics Medical,College of CAPF,Tianjin 300162,China
  • Received:2012-02-09 Online:2012-06-20 Published:2018-12-03

摘要: 称图X是半传递图,如果X的自同构群Aut(X)作用在其顶点集和边集上都传递,但作用在其弧集上非传递。本文证明了qp2(其中q<p均为奇素数)阶连通4度半传递图同构于qp2阶亚循环群的一个正规Cayley图,且该图还同构于一个紧密连接图,同时决定了其自同构群的阶与可解性。

关键词: Cayley图, 半传递图, 自同构群, 紧密连接图

Abstract: A graph X is said to be a half-transitive graphif its full automorphism group denoted by Aut(X) acts transitively on itsvertex set and edge set,but not on its arc set.In this paper,the connected half-transitive tetravalent graphs of order qp2(q<p and are all odd primes)are proved to be isomorphic to a Normal Cayley graph of a metacyclic group,and the graph is also isomorphic to some tightly attached graph.For the automorphism of such graphs,its order and solvability are determined finally.

Key words: Cayley graph, half-transitive graph, full automorphism group, tightly attached graphs

中图分类号: 

  • O157
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