阶为八倍奇素数的边本原图
Edge-Primitive Graphs of Order Eight Times an Odd Prime
DOI: 10.12677/PM.2022.127121, PDF,    科研立项经费支持
作者: 赖子峰：云南财经大学统计与数学学院，云南 昆明
关键词: 边本原图；本原置换群；几乎单型；Edge-Primitive Graph； Primitive Permutation Group； Almost Simple Type
摘要: 称一个图是边本原的，如果其全自同构群在其边集上的作用是本原的。通过Li的研究成果，我们可以得到包含子群的指数为四倍奇素数和八倍奇素数的本原置换群，并且将连通的非平凡边本原图分为了三种情形。本文我们考虑顶点本原和二部本原的情形，刻画阶为八倍奇素数的边本原图。
Abstract: A graph is called edge-primitive, if its automorphism group acts primitively on its edge set. Through Li’s research findings, we can obtain the primitive permutation group with a subgroup of index four times an odd prime and eight times an odd prime, and divide the connected non-trivial edge-primitive graphs into three cases. In this paper, edge-primitive graphs of order eight times an odd prime are characterized by considering the case of vertex-primitive and vertex-biprimitive.
文章引用：赖子峰. 阶为八倍奇素数的边本原图[J]. 理论数学, 2022, 12(7): 1095-1102. https://doi.org/10.12677/PM.2022.127121

参考文献

[1] Li, C.H. (2001) Finite s-arc Transitive Graphs of Prime-Power Order. Bulletin of the London Mathematical Society, 33, 129-137. [Google Scholar] [CrossRef] 
[2] Weiss, R.M. (1973) Kantenprimitive Graphen vom Grad drei. Journal of Combinatorial Theory, Series B, 15, 269-288. [Google Scholar] [CrossRef] 
[3] Giudici, M. and Li, C.H. (2009) On Finite Edge-Primitive and Edge-Quasiprimitive Graphs. Journal of Combinatorial Theory, Series B, 100, 275-298. [Google Scholar] [CrossRef] 
[4] Li, C.H. and Zhang, H. (2011) The Finite Primitive Groups with Soluble Stabilizers, and the Edge-Primitive s-arc Transitive Graphs. Proceedings of the London Mathematical Society, 103, 441-472. [Google Scholar] [CrossRef] 
[5] Guo, S.T., Feng, Y.Q. and Li, C.H. (2015) Edge-Primitive Tetravalent Graphs. Journal of Combinatorial Theory, Series B, 112, 124-137. [Google Scholar] [CrossRef] 
[6] Guo, S.T., Feng, Y.Q. and Li, C.H. (2012) The Finite Edge-Primitive Pentavalent Graphs. Journal of Algebraic Combinatorics, 38, 491-497. [Google Scholar] [CrossRef] 
[7] Pan, J.M. and Wu, C.X. (2020) Finite Hexavalent Edge-Primitive Graphs. Applied Mathematics and Computation, 378, Article ID: 125207. [Google Scholar] [CrossRef] 
[8] Pan, J.M., Huang, Z.H. and Wu, C.X. (2019) Edge-Primitive Graphs of Prime Power Order. Graphs and Combinatorics, 35, 249-259. [Google Scholar] [CrossRef] 
[9] Pan, J.M., Huang, Z.H. and Wu, C.X. (2019) On Edge-Primitive Graphs of Order Twice a Prime Power. Discrete Mathematics, 342, Article ID: 111594. [Google Scholar] [CrossRef] 
[10] Lu, Z.P. (2020) On Edge-Primitive 2-Arc-Transitive Graphs. Journal of Combinatorial Theory, Series A, 171, 105. [Google Scholar] [CrossRef] 
[11] Giudici, M. and King, C. (2021) On Edge-Primitive 3-Arc-Transitive Graphs. Journal of Combinatorial Theory, Series B, 151, 282-306. [Google Scholar] [CrossRef] 
[12] 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.
[13] Wilson, R.A. (2009) The Finite Simple Groups. Springer, London. [Google Scholar] [CrossRef] 
[14] 王超. 阶为四倍素数幂的素数度对称图[D]: [硕士学位论文]. 昆明: 云南财经大学, 2020.
[15] Robinson, D.J.S. (1982) A Course in the Theory of Groups. Springer-Verlag, New York. [Google Scholar] [CrossRef] 
[16] Praeger, C.E. (1993) On 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. [Google Scholar] [CrossRef] 
[17] Li, C.H. and Li, X.H. (2019) On Permutation Groups of Degree a Product of Two Prime-Powers. Communications in Algebra, 42, 4722-4743. [Google Scholar] [CrossRef] 
[18] 徐明曜. 有限群初步[M]. 北京: 科学出版社, 2014.
[19] Sibley, T.Q. (2004) On Classifying Finite Edge Colored Graphs with Two Transitive Automorphism Groups. Journal of Combinatorial Theory, Series B, 90, 121. [Google Scholar] [CrossRef] 
[20] 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] 
[21] Li, C.H., Praeger, C.E., Venkatesh, A. and Zhou, S.M. (2002) Finite Locally-Quasiprimitive Graphs. Discrete Mathematics, 246, 197-218. [Google Scholar] [CrossRef] 
[22] Cameron, P.J. (1981) Finite Permutation Groups and Finite Simple Groups. Bulletin of the London Mathematical Society, 13, 1-22. [Google Scholar] [CrossRef] 

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