有限非交换单群上的5度2-传递Cayley图
Pentavalent 2-Transitive Cayley Graphs on Finite Nonabelian Simple Groups
DOI: 10.12677/AAM.2018.75071, PDF,    国家自然科学基金支持
作者: 凌 波：云南民族大学数学与计算机科学学院，云南 昆明；刘响林：广西大学广西大学行健文理学院，广西 南宁
关键词: 对称图；单群；自同构群；正规Cayley图；Symmetric Graph； Simple Group； Automorphism Group； Normal Cayley Graph
摘要: 称Cayley图Γ=Cay（G,S）是正规的，如果G在AutΓ中正规。本文研究有限非交换单群上的连通5度2-传递Cayley图的正规性，并且证明：所有这样的图要么是正规的，要么G=A39，A59，A119 。这相当于给文献[Europ. J. Combin., 63, 134~145, 2017]推论1.3的部分结果提供了另一种证明方法。
Abstract: A Cayley graph Γ=Cay（G,S）is said to be normal if G is normal in AutΓ . In this paper, we inves-tigate the normality problem of the connected pentavalent 2-transitive Cayley graphs on finite nonabelian simple groups. We prove that all such graphs   are either normal or G=A39，A59 or A119 . This provides another proof for the partial results of Corollary 1.3 of [Europ. J. Combin., 63, 134~145, 2017].
文章引用：凌波, 刘响林. 有限非交换单群上的5度2-传递Cayley图[J]. 应用数学进展, 2018, 7(5): 602-608. https://doi.org/10.12677/AAM.2018.75071

参考文献

[1] 徐明曜. 有限群导引(下) [M]. 第二版. 北京: 科学出版社, 1999.
[2] Xu, M.Y. (1998) Automorphism Groups and Isomorphisms of Cayley Digraphs. Discrete Mathematics, 182, 309-319.
[Google Scholar] [CrossRef] 
[3] Li, C.H. (1996) Isomorphisms of Finite Cayley Graphs. The University of Western Australia, Perth.
[4] Xu, S.J., Fang, X.G., Wang, J., et al. (2005) On Cubic s-Arc Transi-tive Cayley Graphs of Finite Simple Groups. European Journal of Combinatorics, 26, 133-143.
[Google Scholar] [CrossRef] 
[5] Xu, S.J., Fang, X.G., Wang, J., et al. (2007) 5-Arc Transitive Cu-bic Cayley Graphs on Finite Simple Groups. European Journal of Combinatorics, 28, 1023-1036.
[Google Scholar] [CrossRef] 
[6] Fang, X.G., Wang, J. and Zhou, S.M. (2016) Tetravalent 2-Transitive Cayley Graphs of Finite Simple Groups and Their Automorphism Groups. arXiv:1611.06308v1
[7] Zhou, J.X. and Feng, Y.Q. (2010) On Symmetric Graphs of Valency Five. Discrete Mathematics, 310, 1725-1732.
[Google Scholar] [CrossRef] 
[8] Du, J.L., Feng, Y.Q. and Zhou, J.X. (2017) Pentavalent Sym-metric Graphs Admitting Vertex-Transitive Non-Abelian Simple Groups. European Journal of Combinatorics, 63, 134-145.
[Google Scholar] [CrossRef] 
[9] 徐明曜. 有限群导引(上) [M]. 第二版. 北京: 科学出版社, 1999.
[10] Suzuki, M. (1985) Group Theory II. Springer-Verlag, New York.
[11] Praeger, C.E. (1992) An O’Nan-Scott Theorem for Finite Quasiprimitive Permutation Groups and an Application to 2-Arc-Transitive Graphs. Journal of the London Mathematical Society, 47, 227-239.
[12] Li, C.H. and Pan, J.M. (2008) Finite 2-Arc-Transitive Abelian Cayley Graphs. European Journal of Combinatorics, 29, 148-158.
[Google Scholar] [CrossRef] 
[13] Guo, S.T. and Feng, Y.Q. (2012) A Note on Pentavalent s-Transitive Graphs. Discrete Mathematics, 312, 2214-2216.
[Google Scholar] [CrossRef] 
[14] Zhou, J.X. (2008) Symmetry of Graphs and Embeddings of Graphs into Surfaces. Beijing Jiaotong University, Beijing.
[15] Roney-Dougal, C.M. (2005) The Primitive Permutation Groups of Degree Less Than 2500. Journal of Algebra, 292, 154-183
[Google Scholar] [CrossRef] 
[16] Bosma, W., Cannon, C. and Playoust, C. (1997) The MAGMA Algebra System I: The User Language. Journal of Symbolic Computation, 24, 235-265.
[Google Scholar] [CrossRef] 
[17] Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A. and Wilson, R.A. (1985) Atlas of Finite Groups. Oxford University Press, London/New York.

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