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.

这个项目旨在利用有限简单群的知识来解决图对称性的问题。对象的对称性是由群编码的，这使得代数工具可以用来研究图形。主要影响将在纯数学领域，如图论和群论，通过获得新的分类和结构。预期的成果包括提供新的建设和高度对称的图形分类，并提高知识和理解的局部对称性的图形更高的价，使他们成为以及理解的价三的情况下。