项目名称: 图谱理论的研究及其在复杂网络中的应用
项目编号: No.11471121
项目类型: 面上项目
立项/批准年度: 2015
项目学科: 数理科学和化学
项目作者: 束金龙
作者单位: 华东师范大学
项目金额: 62万元
中文摘要: 图谱理论是图论的一个重要的研究方向,对图的谱性质与图结构之间关系的研究不仅能够促使图谱理论自身的发展,而且一直为许多其他领域的发展提供着有力的工具。近年来,其更是在蓬勃的复杂网络的定量研究中扮演着重要的角色。本项目主要研究图的谱性质与图结构之间的联系,解决一些具有挑战性的代数图论问题。同时,关注图的谱性质在复杂网络中的应用。即,1.应用图的谱性质有效地解决复杂网络中的一些重要的问题,特别是网络的社团性质,网络同步与控制。2.研究图谱的界,以及按照他们的谱进行分类和排序。3.研究图的多项式的系数。4.研究图的距离矩阵的零维数、谱唯一性及最小根等问题。
中文关键词: 代数图论;复杂网络;图的谱
英文摘要: Graph spectral theory is a main research field of graph theory. Studying the relation between the spectral properties and the structural properties of graphs not only promotes the development of the spectral theory, but also provides a strong tool for applying this theory to the other field. In recent years, it plays a key role in the quantitative research in the theory of complex network. In this project we mainly study the relationship between the properties of graph spectral and structure, and we also want to solve some challenging algebraic graph problems. Furthermore, we care the applications of graph spectral theory in the theory of complex network. Such as: 1. To efficiently solve some key problems of complex network, espencially the community properties, synchronous properties and control properties of a network. 2. To study the bounds of spectral radius of graphs and order, classification graphs by it. 3. To study the coefficient of the polynomial of graph matrices. 4. To study the nullity, the least eigenvalue of the distance matrix of a graph and the graph determined by its distance spectra.
英文关键词: Algebraic graph theory;The complex network;Graph spectra