图的基于距离的拓扑指标及若干相关问题

项目名称： 图的基于距离的拓扑指标及若干相关问题

项目编号： No.11201227

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： 许克祥

作者单位： 南京航空航天大学

项目金额： 22万元

中文摘要： 图的各种拓扑指标的研究是化学图论中的热点问题。我们拟研究图的基于距离的几类拓扑指标，如广泛研究的Wiener 指标和hyper-Wiener 指标、Harary 指标、Kirchhoff指标及最近研究的偏心距离和（EDS）等。根据最新研究，图的Zagreb 指标也属于此类拓扑指标。这类指标在化学图论中有着重要的应用，具有很好的数学性质。确定给定图类中关于此类拓扑指标上下界，刻画相应的极图有着深刻的理论和实际意义。研究此类拓扑指标之间的内在联系，确定其数量关系，以及在此基础上，构造给定图类中关于某几种拓扑指标的极图的统一方法及关于拓扑指标的逆问题，都是化学图论中的重要方向。本项目在分析同类研究的基础上，确定给定参数下关于此类拓扑指标的极图，探究几种拓扑指标之间的数量关系，构造给定图类中关于尽可能多的拓扑指标的极图的统一方法，我们还将在关于此类拓扑指标的逆问题上做一些深入探讨。

中文关键词： 图；距离；顶点度；极值问题；图谱

英文摘要： The research on various topological indices of graphs is a hot topic in chemical graph theory. We will study on several topological indices of graphs which are based on distance in graph, such as Wiener index, hyper-Wiener index, Harary index and Kirchhoff index which are extensively studied, and eccentric distance sum (EDS) which is recently studied，etc. Zagreb indices are also distance-based topological indices according to the newest researching result. These indices of this kind have some nice mathematical properties and been found some important applications in chemical graph theory. It is fundamental from theoretical and applicable viewpoints to determine the bounds for these topological indices of graphs from some given set and characterize the corresponding extremal graph. There are some other important directions in chemical graph theory, which are to study the inner correlation among several topological indices of graphs and to establish some numerical relationship among them, and based on it to construct some unified approach to determine the extremal graphs in some given set with respect to several topological indices as well as the inverse problem for topological indices. In this research item, based on some excellent known results of this type, we will explore the numerical relation among several

英文关键词： Graph；Distance；Degree of vertex；Extremal problem；spectra of graphs