Journal of Guangxi Normal University(Natural Science Edition) ›› 2010, Vol. 28 ›› Issue (2): 30-33.

Previous Articles     Next Articles

Cubic Cayley Graphs on Three Kinds of Groups with Order 2q2p

XU Shang-jin, SUN Li-min, LIU Cui-ming, BAI Hui-juan   

  1. School of Mathematics and Information Sciences,Guangxi University,Nanning Guangxi 530004,China
  • Received:2010-02-11 Online:2010-06-20 Published:2023-02-07

Abstract: A Cayley (di)graph Γ of a finite group G issaid to be normal if the action of G on V(Γ) by right multiplication isnormal in the full automor-phism group of Γ.This paper mainly researches the mormality of connected cubic Cayley graphs on three kinds ofmetacyclic groups with order 2q2p,where both q＜p are odd primes andq (p-1).In application,the weak 3-CI property of two kinds of groups are determined.The conclusion also involves in the classification of the finite simple groups.

Key words: Cayley graph, normal Cayley graph, weak m CI-property

CLC Number: 

  • O157
[1] 徐尚进,朱雁,邓芸萍.qp阶群陪集图的CI性[J].广西大学学报:自然科学版,2007,32(3):278-281.
[2] ALSPACH B.Point-symmetric graphs and digraphs of prime order and transitive permutation groups of prime degree[J].J Combin Theory:B,1973,15(1):12-17.
[3] DU Shao-fei,WANG Ru-ji,XU Ming-yao.On the normality of Cayleydigraphs of order twice a prime[J].Australas J Combin,1998,18:227-234.
[4] LU Zai-ping,XU Ming-yao.On the normality of Cayley graphs of order pq[J].Australas J Combin,2003,27:81-93.
[5] 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.
[6] FANG Xing-gui,LI Cai-heng,WANG Jie,et al.On cubic Cayleygraphs of finite simple groups[J].Discrete Math,2002,244(1/3):67-75.
[7] XU Shang-jin,FANG Xin-gui,WANG Jie,et al.On cubic s-Arc-transitive Cayley graphs of finite simple groups[J].European J Combin,2005,26(1):133-143.
[8] XU Shang-jin,FANG Xin-gui,WANG Jie,et al.5-Arc transitive cubic Cayley graphs on finite simple groups[J].European J Combin,2007,28(3):1023-1036.
[9] YU Hui-xia,ZHOU Jin-xin,WANG Ling-li.Cubic Cayley graph of order 2p2[J].Advances in Mathematics,2006,35(5):581-589.
[10] 孟庆云,王长群.两类2pq阶3度Cayley图的正规性[J].厦门大学学报:自然科学版,2009,48(1):6-10.
[11] ZHANG Cui,ZHOU Jin-xin,FENG Yan-quan.Automorphisms of cubic Cayley graphs of order 2pq[J].Discrete Math,2009,309(9):2687-2695.
[12] 张远达.有限群的构造[M].北京:科学出版社,1982.
[13] 徐明曜.有限群导引[M].2版.北京:科学出版社,1999.
[14] GORENSTEIN D.Finite simple groups[M].New York:Plenum Press,1982:12-14.
[15] 施武杰.关于单K4群[J].科学通报,1991,36(17):1281-1283.
[16] 张良才,陈顺民.一类2pq2阶群的自同构群[J].海南大学学报:自然科学版,2003,21(4):308-311.
[17] BIGGS N.Algebraic graph theory[M].2nd ed.Cambridge:Cambridge University Press,1993.
[1] LI Jingjian, ZHU Wenying, XIE Yating. One-Regular Cayley Graphs of Valency Odd Prime [J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(2): 121-125.
[2] HUA Xiao-hui, CHEN Li. Isomorphisms and Automorphisms of Coset Graphs [J]. Journal of Guangxi Normal University(Natural Science Edition), 2015, 33(4): 68-72.
[3] XU Shang-Jin, LI Ping-shan, HUANG Hai-hua, LI Jing-jian. 8-Valent 1-Regular Cayley Graphs WhoseVertex Stabilizer is Z4×Z2 [J]. Journal of Guangxi Normal University(Natural Science Edition), 2015, 33(1): 59-66.
[4] XU Shang-Jin, QIN Yan-li, ZHANG Yue-feng, LI Jing-jian. 1-Regular Cayley Graphs of Valency 9 with Elementary Abelian Vertex Stabilizer [J]. Journal of Guangxi Normal University(Natural Science Edition), 2014, 32(4): 66-71.
[5] LI Jing-jian, XU Shang-jin, WANG Rui. 1-Regular Hexavalent Cayley Graphs with Abelian Point Stabilizer [J]. Journal of Guangxi Normal University(Natural Science Edition), 2013, 31(2): 51-54.
[6] XU Shang-jin, ZHANG Xiao-jun, KANG Zhe, LI Jing-jian. Tetravalent Connected Half-transitive Graphs of Order qp2 [J]. Journal of Guangxi Normal University(Natural Science Edition), 2012, 30(2): 54-58.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] CHEN Yong-qi, BAI Ke-zhao, KUANG hua, KONG Ling-jiang, LIU Mu-ren. Effect of Internal Layout on the Pedestrian Evacuation in the Classroom[J]. Journal of Guangxi Normal University(Natural Science Edition), 2011, 29(1): 1 -4 .
[2] XU Lun-hui, YE Fan. Acceleration Noise Model Based on Horizontal,Vertical and LateralAcceleration[J]. Journal of Guangxi Normal University(Natural Science Edition), 2011, 29(1): 5 -9 .
[3] YANG Li, KONG Ling-jiang. Capillary Force between Microparticles[J]. Journal of Guangxi Normal University(Natural Science Edition), 2012, 30(1): 1 -4 .
[4] HE Qing, LIU Jian, WEI Lianfu. Single-Photon Detectors as the Physical Limit Detections of Weak Electromagnetic Signals[J]. Journal of Guangxi Normal University(Natural Science Edition), 2022, 40(5): 1 -23 .
[5] BAI Ke-zhao, LUO Xu-dong, KONG Ling-jiang, LIU Mu-ren. Cellular Automaton Model of Date Transmission with Open Boundary Condition[J]. Journal of Guangxi Normal University(Natural Science Edition), 2010, 28(3): 1 -4 .
[6] XU Lun-hui, LIAO Ran-kun. Signal Phasing-Sequence Optimization of Intersection Based on Traffic Track[J]. Journal of Guangxi Normal University(Natural Science Edition), 2010, 28(3): 5 -9 .
[7] WANG Xiu-xin, QIN Li-mei, NONG Jing-hui, LIANG Zong-jin, ZHU Qi-jiang. Land Surface Temperature Retrieval with Mono-window Algorithm in Karst City[J]. Journal of Guangxi Normal University(Natural Science Edition), 2010, 28(3): 10 -14 .
[8] LI Yu-fang, ZHANG Jun-jian. Strong Consistency of the Regression Weighted Function Estimator for Negatively Associated Samples[J]. Journal of Guangxi Normal University(Natural Science Edition), 2010, 28(3): 15 -19 .
[9] JIA Bao-hua. A Strictly Stationary Associated Random Sequence Which Unsatisfythe Central Limit Theorem[J]. Journal of Guangxi Normal University(Natural Science Edition), 2010, 28(3): 20 -23 .
[10] CHEN Cui-ling, LI Ming, LIANG Jia-mei, LI Lüe. A Class of New Conjugate Gradient Method and Its Convergence Property Under the Wolfe Line Search[J]. Journal of Guangxi Normal University(Natural Science Edition), 2010, 28(3): 24 -28 .
Copyright © Journal of Guangxi Normal University(Natural Science Edition), All Rights Reserved.
Tel: 0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
Powered by Beijing Magtech Co. Ltd