谱图论

This project is concerned with the use of algebraic techniques in the study of graphs and combinatorics. The mainly deal with the spectral properties of adjacency matrices and Laplacian matrices of graphs and the connection between the spectra.of a graph and the other properties of a graph Some inequalities involving the largest and smallest eigenvalues of a graph are given. The theory of graph spectra have important applications in.quantum chemistry, electronic ngineering, computer net, and information science. Some books have been published, which are.relevant to the theory of graph pectra.We translate properties of graphs into algebraic properties and then using the results and methods of algebra， number theory, and topology, to deduce some interesting results of graphs.

本项目主要研究图的邻接谱和拉普拉斯谱的性质。. 用代数的方法和技巧研究图的拓扑性质，组合性质和统计性质。找出它们之间的联系，从而研究图的结构，得到新的图的不变量和某些特殊图类的完全不变量。这对于揭示图的本质属性有着十分重要的意义。