奇数阶的4度2-弧传递图
Tetravalent 2-Arc-Transitive Graphs of Odd Order
DOI: 10.12677/PM.2021.1112221, PDF,    科研立项经费支持
作者: 李晓琪, 赖子峰：云南财经大学统计与数学学院，云南 昆明
关键词: 2-弧传递图；自同构群；拟本原；几乎单群；2-Arc-Transitive； Automorphism Groups； Quasiprimitive； Almost Simple Group
摘要: 设Γ是一个连通图，G≤Aut(Γ)，如果G作用在图的2-弧集上是传递的，则称Γ为(G,2)-弧传递图。在本文中，我们通过研究G作用在VΓ上拟本原来刻画奇数阶4度(G,2)-弧传递图，并且利用陪集图来描述这些图。
Abstract: LetΓ be a connected graph, G≤Aut(Γ). Γ is said to be (G,2)-arc-transitive if G acts transitively on its 2-arcs. In this paper, we characterize tetravalent (G,2)-arc-transitive graphs of odd order by studying the quasiprimitive case of G acting on vertex set of Γ, and a description of these graphs as coset graphs is given.
文章引用：李晓琪, 赖子峰. 奇数阶的4度2-弧传递图[J]. 理论数学, 2021, 11(12): 1987-1992. https://doi.org/10.12677/PM.2021.1112221

参考文献

[1] Gardiner, A. and Praeger, C.E. (1994) On 4-Valent Symmetric Graphs. European Journal of Combinatorics, 15, 375-381. [Google Scholar] [CrossRef] 
[2] Gardiner, A. and Praeger, C.E. (1994) A Characterization of Certain Families of 4-Valent Symmetric Graphs. European Journal of Combinatorics, 15, 383-397. [Google Scholar] [CrossRef] 
[3] Tutte, W.T. (1947) A Family of Cubical Graphs. Mathematical Pro-ceedings of the Cambridge Philosophical Society, 43, 621-624. [Google Scholar] [CrossRef] 
[4] Weiss, R. (1981) The Nonexistence of 8-Transitive Graphs. Combinatorica, 1, 309-311. [Google Scholar] [CrossRef] 
[5] Praeger, C.E. (1992) An O’Nan-Scott Theorem for Finite Quaiprimitive Permutation Groups and an Application to 2-Arc-Transitive Graphs. Journal of the London Mathematical Society, 47, 227-239. [Google Scholar] [CrossRef] 
[6] Fang, X.G. and Praeger, C.E. (1999) Finite Two-Arc Transitive Graphs Admitting a REE Simple Group. Communication in Algebra, 27, 3755-3769. [Google Scholar] [CrossRef] 
[7] Fang, X.G. and Praeger, C.E. (1999) Finite Two-Arc Transitive Graphs Admitting a Suzuki Simple Group. Communication in Algebra, 27, 3727-3754. [Google Scholar] [CrossRef] 
[8] Hassani, A., Nochefranca, L.R. and Praeger, C.E. (1999) Two-Arc Transitive Graphs Admitting a Two-Dimensional Projective Linear Group. Journal of Group Theory, 2, 335-354. [Google Scholar] [CrossRef] 
[9] 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] 
[10] Huppert, B. and Lempken, W. (2000) Simple Groups of Order Di-visible by at Most Four Primes. Francisk Skorina Gomel State University, 16, 64-75.
[11] 徐明曜. 有限群导引(上) [M]. 北京: 科学出版社, 1999.
[12] 徐明曜. 有限群导引(下) [M]. 北京: 科学出版社, 1999.
[13] Dixon, J. and Mortimer, D.B. (1997) Permutation Groups. Spring-Verlag, New York. [Google Scholar] [CrossRef] 
[14] Zhou, J.X. (2009) Tetravalent s-Transitive Graphs of Order 4p. Discrete Mathematics, 309, 6081-6086. [Google Scholar] [CrossRef] 
[15] Bosma, W., Cannon, J. and Playoust, C. (1997) The MAGMA Algebra System I: The User Language. Journal of Symbolic Computation, 24, 235-265. [Google Scholar] [CrossRef] 
[16] Li, C.H. (2001) On Finite s-Transitive Graphs of Odd Order. Journal of Combinatorial Theory, Series B, 81, 307-317. [Google Scholar] [CrossRef] 

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