Enumeration and properties of large discrete structures

大型离散结构的枚举和性质

• 批准号: DP180103684
• 负责人: Prof Nicholas Wormald
• 金额: $ 27.24万
• 依托单位: Monash University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2018
• 资助国家: 澳大利亚
• 起止时间: 2018-05-01 至 2023-07-05
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP180103684
• 关键词: Enumeration; properties; large; discrete; structures

This project aims to study a fundamental property of random graphs, by further developing a recently introduced approach to the problem of enumerating graphs with given degrees. Using this new method, the project expects to generate new knowledge on the number of connections that each node has with other nodes in a random graph, and to develop new strategies for counting the graphs or networks with a given property. The project expects to produce new theoretical results as well as enhanced capabilities of mathematical research. Potential benefits arise through the uses of these theoretical combinatorial objects to study naturally occurring networks such as social networks, the network of the world wide web, and chemical compounds.

这个项目的目的是研究随机图的一个基本性质，通过进一步发展最近引入的方法来枚举给定度的图的问题。使用这种新方法，该项目预计将产生关于每个节点与随机图中其他节点的连接数量的新知识，并开发新的策略来计算具有给定属性的图或网络。该项目预计将产生新的理论成果，并提高数学研究的能力。通过使用这些理论组合对象来研究自然发生的网络，如社交网络、万维网网络和化合物，可能会产生潜在的好处。