超图的张量表示及其谱理论研究

项目名称： 超图的张量表示及其谱理论研究

项目编号： No.11471077

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： 常安

作者单位： 福州大学

项目金额： 56万元

中文摘要： 近年来，随着张量特征值理论的建立和完善，使得超图的张量表示及其特征值研究有了坚实的理论基础，从而可以丰富之前以矩阵特征值理论为基础的图谱理论。本项目计划研究超图张量谱及其与超图结构性质之间关系问题。主要内容包括：1. 一致超图的低阶张量表示及其谱问题研究；2. 一致超图的张量谱性质研究；3. 超图张量谱刻画超图的结构性质研究。因为超图的张量谱研究是一个新的研究领域，其中有许多问题有待解决。我们希望通过本项目的研究工作，能够在理论研究和方法创新上有所突破，对图与超图谱理论及其应用研究产生推动作用。

中文关键词： 超图；张量；特征值；结构性质

英文摘要： In the recent years, with the establishment and development of the spectra theory on tensors, the theoretical foundation on the research topic on the tensor representative of hypergraphs and their eigenvalues have been built. Thus, the spectra theory of graphs based on the theory of the eigenvalues of matrices is enriched. This project is going to investigate the tensor spectra of hypergraphs and their connections with the structural properties of hypergraphs. The current project consists of the following three parts. 1. To study the lower order tensor representative of the uniform hypergraphs and their spectra; 2. Investigating the properties of the tensor spectra of the uniform hypergraphs; 3. Depicting the structural properties of hypergraphs by their tensor spectra. There are many problems to be solved because the study on the tensor spectra of hypergraphs is a new topic. We hope that, by carrying out this project, we can make some methodical and theoretical breakthroughes on the problems mentioned above, and make significant progresses on the study of the spectra theory of graphs and hypergraphs and their applications.

英文关键词： Hypergraph;Tensor;Eigenvalue;Structural Property