平方自由阶素数度2-弧正则图
2-Arc-Regular Graphs of Square-Free Order and Prime Valency
DOI: 10.12677/AAM.2018.74046, PDF,   
作者: 丁梦琳：云南财经大学统计与数学学院，云南 昆明
关键词: 自同构群；弧正则图；凯莱图；Automorphism Group； Arc-Regular Graph； Cayley Graph
摘要: 称一个图为s-弧正则图，如果图的全自同构群在图的s弧集上是正则的。Feng等在[1]中证明了素数度的1-弧正则图都是Cayley图，随后出现一些小度数图的研究，见[2][3][4]。本文即确定了平方自由阶素数度的2-弧正则图，其中度数t满足t≡3(mod4)。
Abstract: A graph is called (X,s)-arc regular, if X≤AutΓ is regular on s-arc set. Feng’s paper [1] determined all one-regular graphs of square-free order and prime valent are Cayley graphs. Quite a lot of works with small valency are known, see [2][3][4]. We determined all 2-arc-regular graphs of square-free order and prime valency, where the degreet≡3(mod4).
文章引用：丁梦琳. 平方自由阶素数度2-弧正则图[J]. 应用数学进展, 2018, 7(4): 369-373. https://doi.org/10.12677/AAM.2018.74046

参考文献

[1] Feng, Y.Q. and Li, Y.T. (2011) One-Regular Graphs of Square-Free Order of Prime Valency. European Journal of Combinatorics, 32, 261-275. [Google Scholar] [CrossRef] 
[2] Fang, X., Wang, J. and Xu, M.Y. (2002) On 1-Arc-Regular Graphs. European Journal of Combinatorics, 23, 785-791. [Google Scholar] [CrossRef] 
[3] Feng, Y.Q. and Kwak, J.H. (2004) One-Regular Cubic Graphs of Order a Small Number Times a Prime or Prime Square. Journal of the Australian Mathematical Society, 76, 345-356. [Google Scholar] [CrossRef] 
[4] Feng, Y.Q. and Kwak, J.H. (2007) Cubic Symmetric Graphs of Order a Small Number Times a Prime or a Prime Square. Journal of Combinatorial Theory, Series B, 97, 627-646. [Google Scholar] [CrossRef] 
[5] Pan, J.M., Ding, S.Y. and Liu, Y. (2014) Finite Arc-Regular Graphs of Prime Valency. Scientia Sinica Mathematica, 44, 307-315. [Google Scholar] [CrossRef] 
[6] Li, C.H., Lu, Z.P. and Wang, C.X. (2015) On Edge-Transitive Graphs of Square-Free Order. European Journal of Combinatorics, 22, 41-46. [Google Scholar] [CrossRef] 
[7] Ling, B. and Lou, B.G. (2017) Arc-Transitive Cubic Graphs of Order Four Times an Odd Square-Free Integer. Journal of Algebra and Its Applications, 16, 213-225. [Google Scholar] [CrossRef] 
[8] 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] 
[9] Biggs, N. (1992) Algebraic Graph Theory. 2nd Edition, Cambridge University Press, New York.
[10] Dickson, L.E. (1958) Linear Groups with an Expositions of the Galois Field Theory. Dover.

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