Graph symmetry and simple groups

图对称性和简单群

• 批准号: DP190101024
• 负责人: Prof Michael Giudici
• 金额: $ 16.85万
• 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: 2019
• 资助国家: 澳大利亚
• 起止时间: 2019-02-20 至 2023-02-19
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP190101024
• 关键词: Graph; symmetry; simple; groups

This project aims to use knowledge of finite simple groups to tackle problems in graph symmetry. The symmetry of an object is encoded by a group, and this allows tools from algebra to be used to study graphs. The main impact will be in areas of pure mathematics such as graph theory and group theory by obtaining new classifications and constructions. Expected outcomes include providing new constructions and classifications of highly symmetric graphs, and an improved knowledge and understanding of local symmetries for graphs of higher valencies so that they become as well understood as the valency three case.

该项目旨在利用有限单群的知识来解决图对称问题。对象的对称性由群编码，这使得代数工具可以用于研究图形。通过获得新的分类和构造，主要影响将出现在纯数学领域，例如图论和群论。预期成果包括提供高度对称图的新构造和分类，以及提高对更高化合价图的局部对称性的认识和理解，以便它们像化合价三情况一样被理解。