图谱理论中若干问题的研究

项目名称： 图谱理论中若干问题的研究

项目编号： No.11201156

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 刘木伙

作者单位： 华南农业大学

项目金额： 22万元

中文摘要： 图的谱理论是组合数学与代数图论中研究的一个重要课题，本课题将对图谱的理论及其应用中的若干问题进行研究，研究的主要问题如下：在图谱理论方面，我们将致力于寻找一般且简便的谱半径的排序方法，尝试通过图本身的某些参数的比较来达到谱半径的比较目的，探索由已知"由谱所确定"的图类(整谱图)出发如何构造新的"由谱所确定"的图类(整谱图)的方法，尝试研究给定度序列的图类中具有最大(最小)谱半径的极图刻划，并以此为基础来发掘新的图谱的优超定理；在图谱应用方向，将重点研究与图谱有密切联系的各类化学指数的若干问题，如探索某些化学指数的一般且简便的排序方法，尝试刻划给定度序列的图类中具有最大(最小)化学指数的极图，并寻找服从优超理论的新的化学指数.

中文关键词： 图谱；化学指数；极值理论；优超理论；标尺定理

英文摘要： The graph spectral theory is an important research subject in combinatorics and algebraic graph theory, this project will study some problems on the theory and its application of spectra of graphs. And the main task of this project will focus on the followings: in the aspect of spectra of graphs, we try to search a general and convenient approach to the order of the spectral radii of graphs, which will transfer the comparison of spectral radii to the comparision of some parameters of graphs, we also investigate the method to construct new graphs determined by their spectra (respectively, new integral spectral graphs) from the original graphs determined by their spectra (respectively, original integral spectral graphs), and study the extremal graphs with the maximum (minimum) spectral radii in the class of connected graphs with given degree sequences，based on which we shall try to discover new majorization theorems in the spectra of graphs; in the aspect of the applications of spectra of graphs, we focus on some problems of different kinds of chemical indices, which are closely connected with the spectra of graphs. In this direction, we shall investigate the general and convenient approach to the order of some chemical indices, study the extremal graphs with the maximum (

英文关键词： Graph spectrum；Chemical omdex；Extremal theory；Majorization theory；Rulers' theorem