图的能量与排序问题研究

项目名称： 图的能量与排序问题研究

项目编号： No.11261047

项目类型： 地区科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 火博丰

作者单位： 青海师范大学

项目金额： 45万元

中文摘要： 本项目研究图能量与排序问题。包括一般图的能量极值问题和极值图的刻划；讨论一般图的能量排序的可能性；对一般二部图或单圈图拟序不可比问题的更深入研究和拟序不可比的一般二部图或单圈图能量的比较与结构的刻划；等能量树的构造；能量概念的广义理解及在此基础上的研究；图能量与基于图谱的图变量的关系；图能量在图运算下变化的规律及图与子图的能量的联系；图的其它拓朴指标如Hosoya指标的排序与能量排序的关系等。充分利用我们在能量的极值图和拟序不可比问题研究中找到的新方法，并为研究图能量的排序问题探索新的方法与路径。

中文关键词： 能量；排序；极图；图谱；Zagreb 指标

英文摘要： It is the main aim of the project to reserch the graph energy and ordering problem. It includes that the problem of the extremal energies of general graphs and the characterization of the extremal graphs, the possibility to order energy on general graphs,the investigation into qusi-order incomparable on general bipartite or unicyclic graphs and the characterization of the structures for general bipartite or unicyclic graphs that are quasi-order incomparable, finding a way to search or to construct the trees that have equal energy, considering the concept of energy in different point of view and discussing the related topics based the new point, investigating the relation between graph energy and the variants based graph spectrum, investigating the variance about graph energy under certain graph operation and the relation between the energy of a graph and its subgraphs, discussing the relation on order of graph energy and the order of the other topological index , such as Hosoya index. Utilizing the new methods having been found in our work on certain extremal graph of energy as well as related quasi-order incomparable problems, we want to explore the way to order graph energy.

英文关键词： energy；order；extremal graph；graph spectrum；Zagreb indices