4pqn阶3度对称图的分类
A Classification on Cubic Symmetric Graphs of Order 4pqn
DOI: 10.12677/PM.2019.910139, PDF,    国家自然科学基金支持
作者: 王 超：云南财经大学统计与数学学院，云南 昆明
关键词: 对称图；局部本原；拟本原；二部拟本原；几乎单；Symmetric Graph； Locally Primitive； Quasiprimitive； Bi-Quasiprimitive； Almost Simple
摘要: 设Γ是一个连通图，G≤Aut(Γ)，如果G作用在VΓ上是拟本原或顶点二部拟本原的，则称Γ是G-基图。在本文中，我们将4pqn阶3度对称G-基图，其中p < q为奇素数，n≥1。
Abstract: Let Γ be a connected graph and G≤Aut(Γ). Then Γ is called a G-basic graph, if G is quasiprimitive or bi-quasiprimitive on VΓ. In this paper, we determine cubic symmetric G-basic graphs of order 4pqn, where p < q are odd primes, and n≥1.
文章引用：王超. 4pqn阶3度对称图的分类[J]. 理论数学, 2019, 9(10): 1132-1138. https://doi.org/10.12677/PM.2019.910139

参考文献

[1] Chao, C.Y. (1971) On the Classification of Symmetric Graphs with a Prime Number of Vertices. Transactions of the American Mathematical Society, 158, 247-256. [Google Scholar] [CrossRef] 
[2] Cheng, Y. and Oxley, J. (1987) On Weakly Symmetric Graphs of Order Twice a Prime. Journal of Combinatorial Theory, Series B, 42, 196-211. [Google Scholar] [CrossRef] 
[3] Wang, R.J. and Xu, M.Y. (1993) A Classification of Symmetric Graphs of Order 3p. Journal of Combinatorial Theory, Series B, 58, 197-216. [Google Scholar] [CrossRef] 
[4] Feng, Y.Q. and Kwak, J.H. (2006) Cubic Symmetric Graphs of Order Twice an Odd Prime Power. Journal of the Australian Mathematical Society, 81, 153-164. [Google Scholar] [CrossRef] 
[5] Feng, Y.Q. and Kwak, J.H. (2007) Cubic Symmetric Graphs of Or-der a Small Number Times a Prime or a Prime Square. Journal of Combinatorial Theory, Series B, 97, 627-646. [Google Scholar] [CrossRef] 
[6] Feng, Y.Q., Zhou, J.X. and Li, Y.T. (2016) Pentavalent Symmetric Graphs of Order Twice a Prime Power. Discrete Mathematics, 339, 2640-2651. [Google Scholar] [CrossRef] 
[7] Hua, X.H., Chen, L. and Xiang, X. (2018) Valency Seven Symmetric Graphs of Order 2pq. Czechoslovak Mathematical Journal, 68, 581-599. [Google Scholar] [CrossRef] 
[8] Lu, Z.P., Wang, C.Q. and Xu, M.Y. (2004) On Semisymmetric Cubic Graphs of Order 6p2. Science in China Series A Mathematics, 47, 1-17.
[9] Zhou, J.X. and Feng, Y.Q. (2010) Tetravalent s-Transitive Graphs of Order Twice a Prime Power. Journal of the Australian Mathematical Society, 88, 277-288. [Google Scholar] [CrossRef] 
[10] Tutte, W.T. (1947) A Family of Cubical Graphs. Mathematical Proceedings of the Cambridge Philosophical Society, 43, 459-474. [Google Scholar] [CrossRef] 
[11] Zhou, J.X. and Feng, Y.Q. (2010) Cubic Vertex-Transitive Graphs of Order 2pq. Journal of Graph Theory, 65, 285-302. [Google Scholar] [CrossRef] 
[12] Huppert, B. and Lempken, W. (2000) Simple Groups of Order Divisible by at Most Four Primes. Francisk Skorina Gomel State University, 16, 64-75.
[13] 徐明耀. 有限群导引(上, 下)[M]. 北京: 科学出版社, 1999.
[14] Dixon, J. and Mortimer, D.B. (1997) Permutation Groups. Spring-Verlag, New York. [Google Scholar] [CrossRef] 
[15] 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] 
[16] 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. [Google Scholar] [CrossRef] 
[17] 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] 
[18] Conder, M. and Dobcsabyi, P. (2002) Trivalent Symmetric Graphs on up to 768 Vertices. Journal of Combinatorial Mathematics and Combinatorial Computing, 40, 41-63.
[19] Giudici, M., Li, C.H. and Praeger, C.E. (2003) Analysing Finite Locally s-Arc-Transitive Graphs. Transactions of the American Mathematical So-ciety, 356, 291-317. [Google Scholar] [CrossRef] 
[20] 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] 

为你推荐