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arc-transitive graphs of Square-free Order with Valency 11

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Algebra Colloquium 2021年第4期28卷 645-654页

作者： Guang Li Bo Ling Zaiping Lu School of Mathematics and Statistics Shandong University of Technology ZiboShandong 255049China School of Mathematics and Computer Science Yunnan Minzu University Kunming 650000China Center for Combinatorics LPMCNankai UniversityTianjin 300071China

In this paper,we present a complete list of connected arc-transitive graphs of square-free order with valency *** list includes the complete bipartite graph K11,11,the normal Cayley graphs of dihedral groups and the g... 详细信息

关键词： arc-transitive graph coset graph normal quotient vertex-stabilizer (almost)simple group

On Pentavalent arc-transitive graphs

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Algebra Colloquium 2018年第2期25卷 189-202页

作者： Jingjian Li Jicheng Ma College of Mathematics and Information Science Guangxi University Nanning 530004 China Guangxi Colleges and Universities Key Laboratory of Mathematics and Its Applications Nanning 530003 China Chongqing Key Laboratory of Group & graph Theories and Applications Chongqing University of Arts and Sciences Chongqing 402160 China

In this paper, a characterization of all pentavalent arc-transitive graphs is given. It is shown that each pentavalent arc-transitive covering graph F is a regular simple or elementary abelian covering graph. In parti... 详细信息

关键词： arc-transitive graph pentavalent graph covering graph

A Note on Locally Primitive arc-transitive graphs of Valency8

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Algebra Colloquium 2024年第4期31卷 541-548页

作者： Fateme Abedi M.Reza Salarian Faculty of Mathematical Sciences and Computer Kharazmi UniversityIran

Let X be a connected G-locally primitive arc-transitive graph for some sub-group G of Aut(X).Suppose that X is a(G,s)-transitive *** this paper,we give a characterization of the vertex-stabilizer G,when X has valency 8.

关键词： arc-transitive graph s-transitive graph (G s)-transitive graph locally prim-itivegraph

Locally-primitive arc-transitive lO-Valent graphs of Square-free Order

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Algebra Colloquium 2018年第2期25卷 243-264页

作者： Guang Li Zaiping Lu Xiaoyuan Zhang Center for Combinatorics LPMC-TJKLC Nankai University Tianjin 300071 China

In this paper, we present a complete classification for locally-primitive arctransitive graphs which have square-free order and valency 10. The classification involves nine graphs and three infinite families of graphs.

关键词： arc-transitive graph locally-primitive graph normal quotient vertexstabilizer (almost) simple group

arc-transitive CUBIC graphS OF ORDER 4_p

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Chinese Annals of Mathematics,Series B 2004年第4期25卷 545-554页

作者： XUMINGYAO ZHANGQINHAI ZHOUJINXIN SchoolofMathematicsandComputerSciences ShanxiTeachersUniversityLinfen041004ShanxiChina SchoolofMathematicsandComputerSciences ShanxiTeachersUniversityLinfen041004ShanxiChina.

In this paper, a complete classification of arc-transitive cubic graphs of order 4p is given.

关键词： arc-transitive graph Cubic s-regular graph Coverings of a graph

Semisymmetric graphs admitting primitive groups of degree 9p

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Science China Mathematics 2015年第12期58卷 2671-2682页

作者： HAN Hua LU ZaiPing College of Science Tianjin University of Technology Center for Combinatorics LPMC-TJKLC Nankai University

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.

关键词： edge-transitive graph arc-transitive graph semisymmetric graph primitive permutation group suborbit

On Locally Primitive graphs of Order 18p

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Chinese Annals of Mathematics,Series B 2015年第6期36卷 919-936页

作者： Hua HAN Zaiping LU Center for Combinatorics LPMC-TJKLC Nankai University College of Science Tianjin University of Technology College of Science Tianjin University of Technology

The authors investigate locally order 18p. It is shown that such a graph the Gray graph and the Tutte 12-cage. primitive bipartite regular connected graphs of is either arc-transitive or isomorphic to one of

关键词： Locally primitive graph arc-transitive graph Normal cover Quasiprimitive group

Nonorientable regular embeddings of graphs of order pq

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Science China Mathematics 2011年第2期54卷 351-363页

作者： WANG FuRon DU ShaoFei School of Information Beijing Wuzi University Beijing 101149 China School of Mathematical Sciences Capital Normal University Beijing 100048 China

In [J. Algeb. Combin. 19(2004), 123-141], Du et al. classified the orientable regular embeddings of connected simple graphs of order pq for any two primes p and q. In this paper, we shall classify the nonorientable regular embeddings of these graphs, where p ≠ q. Our classification depends on the classification of primitive permutation groups of degree p and degree pq but is independent of the classification of the arc-transitive graphs of order pq.

关键词： regular embedding arc-transitive graph permutation group

Two sufficient conditions for non-normal Cayley graphs and their applications

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Science China Mathematics 2007年第2期50卷 201-216页

作者： Jin-xin ZHOU Yan-quan FENG Department of Mathematics Beijing Jiaotong UniversityBeijing 100044China

A Cayley graph Cay(G, S) on a group G is said to be normal if the right regular representation R(G) of G is normal in the full automorphism group of Cay(G, S). In this paper, two sufficient conditions for non-normal Cayley graphs are given and by using the conditions, five infinite families of connected non-normal Cayley graphs are constructed. As an application, all connected non-normal Cayley graphs of valency 5 on A 5 are determined, which generalizes a result about the normality of Cayley graphs of valency 3 or 4 on A 5 determined by Xu and Xu. Further, we classify all non-CI Cayley graphs of valency 5 on A 5, while Xu et al. have proved that A 5 is a 4-CI group.

关键词： Cayley graph normal Cayley graph arc-transitive graph 05C25 20B25