关于图谱理论与符号模式矩阵幂敛性质的研究

项目名称： 关于图谱理论与符号模式矩阵幂敛性质的研究

项目编号： No.11271315

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 于广龙

作者单位： 盐城师范学院

项目金额： 65万元

中文摘要： 图谱理论和符号模式矩阵幂敛性质的研究是图论和组合矩阵论中的研究热点，其不仅与众多的数学领域有密切联系，而且在信息科学、生物学、化学、经济学和理论计算机科学等许多方面都有具体的应用背景。基于前人的基础，我们近来研究了一些子图存在性、图子式 (minor)、结构参数与图的谱之间的关系，进一步探讨了符号模式矩阵的幂敛性质在信息传播方面的应用，刻画了一些特殊矩阵类的基，并且在刻画一般本原非可幂符号模式矩阵的基方面取得了进展，得到一些有意义成果。项目组希望通过本项目的研究，利用代数、组合、拓扑、数论、矩阵论、统计的方法和技巧，从不同的视角研究图的矩阵性质与图的结构性质之间的内在联系；利用图的结构和拓扑性质、组合、数论、统计的方法技巧研究符号模式矩阵的幂敛性质。挖掘和丰富图谱理论和符号模式矩阵幂序列性质的研究工具，以期推动一些新问题的解决，并进一步探索它们的理论与实际应用。

中文关键词： 图谱；符号模式矩阵；基；谱半径；图矩阵

英文摘要： The research about the spectral graph theory and the property of a sign pattern's power sequence becomes a research hotspot in the graph theory and combinatoric matrix theory now, which not only have relations with many fields of mathematics, but also have many applications in communication science, biology chemestry, ecnomics, theoretical computer science. Recently, based on the work of the predecessors, we have studied the relations between the existence of some subgraphs and the graph spectrum, the relations between the existence of some graph minors and the graph spectrum, the relations between the strctural parameters and the graph spectrum as well; we have explored the applications of the property of a sign pattern's power sequece furtherly, determined the base set of some special classes of sign patterns and obtained some signifcant results on the characterizition of the base of the general primitive nopowerful sign patterns. We hope that the internal relations between the graph structure property and matrix property is studied from different viewpoints such as algebraic, combinatoric, toplogy, number theory, matrix theory, statistic method and technology,and so on. With graph structure and toplogy property, we also hope that the property of power sequence of the sign patterns is studied by combinatoric,

英文关键词： Spectra of graphs；sign pattern；base；spectral radius；matrices of graphs