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

• • 上一篇    下一篇

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
[1] MARUSIČ D.Half-transitive groups actions on finite graphs of valency 4[J].J Combin Theory:B,1998,73(1):41-76.
[2] SPARL P.A classification of tightly attachedhalf-arc-tiansitive graphs of valency 4[J].J Combin Theory:B,2008,98(5):1076-1108.
[3] BOUWER I Z.Vertex and edge-transitive,but not 1-transitive,graphs[J].Canad Math Bull,1970,13(2):231-237.
[4] ALSPACH B,XU Ming-yao.1/2-transitive graphs of order 3p[J].J Algebraic Combin,1994,3(4):347-355.
[5] WANG Ru-ji.Half-transitive graphs of order a product of two distinct primes[J].Commun Algebra,1994,22(3):915-927.
[6] WANG Xiu-yun,FENG Yan-quan.Hexavalent half-arc-transitivity graphs of order 4p[J].European J Combin,2009,30(5):1263-1270.
[7] XU Ming-yao.Half-transitive graphs of prime-cube order[J].Journal of Algebraic Combinatorics,1992,1(3):275-282.
[8] 徐明曜.关于半传递图的若干新结果[J].数学进展,1994,23(6):505-516.
[9] FENG Yan-quan,WANG Kai-shun,ZHOU Chui-xiang.Tetravalent half-transitive graphs of order 4p[J].European J Combin,2007,28(3):726-733.
[10] FENG Yan-quan,KWAK J H,ZHOU Chui-xiang.Constructing even radius tightly attached half-arc-transitive gra-phs of valency four[J].J Algebraic Combin,2007,26(4):431-451.
[11] DU Shao-fei,WANG Ru-ji,XU Ming-yao.On the normality of Cayley digraphs of groups of order twice a prime[J].Australas J Combin,1998,18:227-234.
[12] 徐尚进,郭松涛,王丽,等.3p2阶连通4度Cayley图的正规性[J].广西师范大学学报:自然科学版,2009,27(2):30-33.
[13] 徐明曜.有限群导引:上,下册[M].北京:科学出版社,1999.
[14] GORENSTEIN D.Finite simple groups[M].New York:Plenum Press,1982:12-14.
[15] MARUšIČ D,PRAEGER C E.Tetravalent graphs admitting half-transitive group action:alternating cycles[J].J Combin Theory:B,1999,75(2):188-205.
[16] 王磊.半传递图与弧传递图[D].南宁:广西大学数学与信息科学学院,2011.
[1] 白舒伊, 周涛, 彭莎丽, 甘凌方, 詹小秦. 区组传递2-(v,k,λ)设计与非点本原群ScwrSd[J]. 广西师范大学学报（自然科学版）, 2020, 38(4): 59-65.
[2] 李靖建, 朱文英, 解雅婷. 奇素数度的1-正则Cayley图[J]. 广西师范大学学报（自然科学版）, 2019, 37(2): 121-125.
[3] 化小会, 陈利. 陪集图的同构与自同构[J]. 广西师范大学学报（自然科学版）, 2015, 33(4): 68-72.
[4] 李靖建, 徐尚进, 王蕊. 具有交换点稳定子群的6度1-正则Cayley图[J]. 广西师范大学学报（自然科学版）, 2013, 31(2): 51-54.
[5] 钟祥贵, 李勇刚, 张福生, 吴勇. 自同构群阶为16p1p2…pr的有限幂零群[J]. 广西师范大学学报（自然科学版）, 2013, 31(2): 58-63.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 广西师范大学学报（自然科学版）编辑部
地址：广西桂林市三里店育才路15号　邮编：541004
电话：0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发