Factorisation of Finite Groups and Graphs

有限群和图的因式分解

• 批准号: DP0449429
• 负责人: Prof Cai-Heng Li
• 金额: $ 21.18万
• 依托单位: The University of Western Australia
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2004
• 资助国家: 澳大利亚
• 起止时间: 2004-02-04 至 2007-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0449429
• 关键词: Factorisation; Finite; Groups; Graphs; Factorisation; Finite; Groups; Graphs

The combinatorial structure of a graph is strongly influenced by its symmetry, and the symmetry is described precisely by its group of automorphisms. Interplay between actions of the automorphism group on vertices, edges, and other configurations, reveals important graph structure, especially the existence of graph factorisations. In turn, a group factorisation arises whenever a group has two independent transitive actions, and these arise in particular while determining graph automorphism groups, and graph factorisations. We will classify families of group factorisations, especially for simple groups, and apply this to establish a theory of symmetrical graph factorisations, and to study Cayley graphs and 2-closures of permutation groups.

图的组合结构受其图表的强烈影响 对称性，对称性正是由其群体描述的 自动形态。自动形态群体的行动之间的相互作用 顶点，边缘和其他配置揭示了重要的图形 结构，尤其是图形分解的存在。反过来，只要组有两个 独立的及时行动，特别是出现 确定图形自动形态组和图形分解。我们将对群体分解的家庭进行分类，尤其是对于简单的群体，并将其应用于建立对称图的理论 分解，并研究置换群体的Cayley图和2个斜率。