三角树图和k4树图的hosoya指标和merrifield-simmons指标分析-ho soya index and merrifield - simmons index analysis of triangle tree and k4 tree.docxVIP

三角树图和K4树图的Hosoya 指标和Merrifield-Simmons 指标研究中文摘要分子拓扑学有着严格的理论体系，近年来，越来越多的数学家和化学家 利用图论知识解决分子拓扑指数的问题. 在各种分子拓扑指数中，Hosoya 指标 和Merrifield-Simmons 指标是两个比较重要的指标，分别用来研究分子图的匹 配总数和独立集总数，它们与分子的总π-电子能，沸点等物理化学性质有密切 的关系. 因此近年来，许多数学家和化学家开始研究Hosoya 指标和Merrifield- Simmons 指标. 其中给定图类的Hosoya 指数和Merrifield-Simmons 指数的排序 问题以及极值图的刻画是一个重要的研究方向，特别是树. 定义Gk 为含k个 三角形的连通图，并且任意两个三角形之间最多有一个公共点，称为三角树 图. 定义T?为含?个K4的连通图，并且任意两个K4之间最多有一个公共点，称 为K4树图. 本文主要研究Gk 和T?，并与树已有的结果进行比较. 并推测是否可 以推广到其他完全图的树图.本文第一章基本知识主要介绍了三角树图，K4树图的定义. 同时，给出 了Hosoya 指标和Merrifield-Simmons 指标的相关背景及定义. 并且简述了所研 究的三角树图以及K4树图的目的. 第二章分别给出了三角树图的Hosoya 指 标和Merrifield-Simmons 指标的算法，并给出了应用. 第三章主要介绍三角 树图的Hosoya指标和Merrifield-Simmons 指标的最大界和最小界，确定了给定 直径下的三角树图的指标界，同时给出了证明与计算. 第四章给出了K4树图 的Hosoya 指标和Merrifield-Simmons 指标的算法，并通过算法求解两个特殊 的K4树图. 第五章总结了全文，并给出对三角树图，K4树图的展望.关键词: Hosoya 指标，Merrifield-Simmons 指标，三角树图，K4 树图， 直径，算法.IOn the Hosoya index and the Merrifield-Simmons index of Tree-triangle graphs and K4-Tree graphsAbstractThe molecular topology has formed a set of strict theory system. In recent years, more and more mathematicians and chemists use the knowledge of graph theory to solve the problem of molecular topological index. Many topology indices have been studied directly. Among these indices, the Hosoya index and the Merrifield-Simmons index are important two indices, which are used to study the total number of matches of molecular graphs and independent sets, respectively. Both the Hosoya index and the Merrifield-Simmons index have close relationships with the physical and chemical properties, such as the total π-electronic energy of molecular and the boiling point. Therefore, many mathematicians and chemists have began to study them. And ordering problem and characterizing of the extremal graphs are an important research issue, especially for the tree. Let Gk be a connected graph with k triangles such that each pair of triangles has at most one common vertex. The graph Gk is called Tree-triangle. Let T? be a connected graph with ? K4 s