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Semisymmetric graphs admitting primitive groups of degree 9p

Semisymmetric graphs admitting primitive groups of degree 9p
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摘要 Let Γ be a connected regular bipartite graph of order 18 p, where p is a prime. Assume that Γ admits a group acting primitively on one of the bipartition subsets of Γ. Then, in this paper, it is shown that eitherΓ is arc-transitive, or Γ is isomorphic to one of 17 semisymmetric graphs which are constructed from primitive groups of degree 9p. Let Γ be a connected regular bipartite graph of order 18 p, where p is a prime. Assume that Γ admits a group acting primitively on one of the bipartition subsets of Γ. Then, in this paper, it is shown that eitherΓ is arc-transitive, or Γ is isomorphic to one of 17 semisymmetric graphs which are constructed from primitive groups of degree 9p.
作者 HAN Hua LU ZaiPing
机构地区 College of Science Center for Combinatorics
出处 《Science China Mathematics》 SCIE CSCD 2015年第12期2671-2682,共12页 中国科学：数学（英文版）
基金 supported by National Natural Science Foundation of China(Grant Nos.11271267 and 11371204)
关键词 edge-transitive graph arc-transitive graph semisymmetric graph primitive permutation group suborbit 半对称图 群体 二部图 正则 连通 素数 子集 同构
分类号 O157.5 [理学—基础数学]
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  • 1LU Zaiping, WANG Changqun & XU MingyaoLMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China,Department of Mathematics, Zhengzhou University, Zhengzhou 450052, ChinaPresent address: Department of Mathematics, Qufu Normal University, Qufu 273165, China..On semisymmetric cubic graphs of order 6p^(2)[J].Science China Mathematics,2004,47(1):1-17. 被引量：12
  • 2Goldschmidt,D. M.Automorphisms of trivalent graphs[].Annals of Mathematics.1980
  • 3Du Shaofei,XU Mingyao.A classification of semisymmetric graphs of order 2pq, Com[].Communications in Algebra.2000
  • 4Titov,V. K.On symmetry in graphs, Voprocy Kibernetiki 9150, Proc.of Hall Union Seminar on Combinatorial Mathematices (in Russian), part 2, Nauka[].Moscow.1975
  • 5Bouwer,I. Z.On edge but not vertex transitive cubic graphs, Canad.Math[].Bulletin.1968
  • 6Folkman,J.Regular line-symmetric graphs, J.Comb[].Theory Ser B.1967
  • 7Ivanov,A. V.On edge but not vertex transitive regular graphs, Comb[].Annals of Discrete Mathematics.1987
  • 8Bouwer,I. Z.On edge but not vertex transitive regular graphs, J.Comb[].Theory Ser B.1972
  • 9Cameron,P. J.Finite permutation groups and finite simple groups, Bull[].London Mathematical Society.1981

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Science China Mathematics
2015年 第12期

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