| 6度1-正则Cayley图 |
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| 引用本文： | 李靖建,徐尚进,杨旭. 6度1-正则Cayley图[J]. 纯粹数学与应用数学, 2013, 0(5): 472-476 |
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| 作者姓名： | 李靖建 徐尚进 杨旭 |
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| 作者单位： | [1]云南大学数学与统计学院,云南昆明650031 [2]广西大学数学与信息科学学院,广西南宁530004 |
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| 基金项目： | 国家自然科学基金（10961004,11226141,11361006）;广西自然科学基金（2013GXNSFAA019018,2013GxNSFBA019018）. |
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| 摘 要： | 试图对6度1-正则Cayley图给一个完全分类．利用无核的概念将图自同构群归结到对称群S6的子群．然后根据1-正则图的性质构造出所有可能的具有非交换点稳定子群的无核6度1-正则Cayley图，进一步证明了构造出的图都是有核的，由此给出了这一类图的一个完全分类．
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| 关 键 词： | 1-正则 Cayley图 无核 |
1-regular Cayley graphs of valency 6 |
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| Li Jingjian,Xu Shangjin,Yang Xu. 1-regular Cayley graphs of valency 6[J]. Pure and Applied Mathematics, 2013, 0(5): 472-476 |
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| Authors: | Li Jingjian Xu Shangjin Yang Xu |
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| Affiliation: | 1. School of Mathematics and Statistics, Yunnan University, Kunming 650031, China; 2. School of Mathematics and Information Sciences, Guangxi University, Nanning 530004, China) |
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| Abstract: | This paper is trying to give a complete classification of 1-regular Cayley graphs of valency 6. By the definition of core-free, this paper reduces the graph automorphism group to a subgroup of symmetric group S6. Furthermore, by the properties of 1-regular graph, this paper constructs all the 1-regular Cayley graphs with nonabelian stabilizers and proves that every such graph is not core-free. Thus a classification of such graphs is given. |
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| Keywords: | 1-regular Cayley graph core-free |
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