图的电阻距离理论及应用研究

项目名称： 图的电阻距离理论及应用研究

项目编号： No.11201404

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： 杨玉军

作者单位： 烟台大学

项目金额： 23万元

中文摘要： 近十几年来，一个新的图上的内在度量- - 电阻距离引起了人们的广泛关注。它等同于电网络中的等效电阻,并且在化学、网络分析及生态学等多个领域有着广阔的应用背景，其研究工作受到广泛重视。基于此，本项目将研究图的电阻距离理论及其在化学和生态学中的应用。具体包括：图扰动对电阻距离的影响；关于图的平均电阻距离的类似于4/3猜想的结论；拓扑相关的S,T-同分异构体的电阻距离和Kirchhoff指标的比较；若干特殊进化图的遗传相关性的计算。 我们的工作将进一步丰富和发展图的电阻距离理论，为电阻距离计算提供新方法，为网络设计和理解拓扑对分子结构性质的影响提供新依据,并在一定程度上打破遗传相关性这个制约进化图理论发展的瓶颈。本研究将对电阻距离理论特别是电阻距离的计算，以及与电阻距离相关的若干重要问题的计算产生重要的推动作用，同时为网络分析、量子化学和进化生态学提供重要的理论依据。

中文关键词： 电阻距离；Kirchhoff指标；S;T-同分异构体；平均电阻距离；HOMO-LUMO能隙

英文摘要： In recent years, a new intrinsic graph metric，resistance distance，has been widely concerned. It is equivalent to the effective resistance in electrical networks, and has been applied widely in many fields such as chemistry, network analysis and ecology. Thus much attention has been paid on the research of it. So in this proposal, we will study the theory of resistance distances and its applications in chemistry and ecology, including: the effect of graph perturbations on resistance distance; result on average resistance distance analogous to the four-thirds conjecture; comparison of resistance distances and Kirchhoff indices of S,T-isomers; and computation of genetic relatedness of some special evolutionary graphs. Our work will enrich and develop the resistance distance theory, provide new methods for computing resistance distances, provide a new basis for network design and for understanding the topological effect on molecular structure properties, and break the bottleneck caused by genetic relatedness that restricts the development of evolutionary graph theory in some degree. This study will play an important role in prompting the development of resistance distance theory, especially the computation of resistance distances, and the computation of other important problems relating to resistance distance. Mea

英文关键词： resistance distance；Kirchhoff index；S;T-isormers；average resistance distance；HOMO-LUMO gap