图的第一几何—算数指数的研究

发布时间：2018-05-01 10:11

本文选题：拓扑指数 + 第一几何-算数指数　；参考：《中北大学》2017年硕士论文

【摘要】：拓扑指数是化学图论中一个非常重要的研究课题,其研究和发展前景非常广泛.它在化学的分子结构中有重要的应用.在这篇文章中,首先,我们给出了第一几何-算数指数关于线图、全图和细分图的计算方法;其次,我们给出了第一几何-算数指数关于线图、全图和细分图的极值及其对应的极图问题.在第一章中,讲了第一几何-算数指数研究的历史过程,给出了一些基本的知识、相关的结果及此文的主要结果.在第二章中,首先给出了第一几何-算数指数关于线图、全图和细分图的计算方法;通过简化第一几何-算数指数在线图和全图达到上下界的条件,得到了线图和全图其第一几何-算数指数上下界的精确值,且刻画了达到极值时相应的极图;补充了第一几何-算数指数在细分图中上下界的极值,且刻画了达到极值时相应的极图.
[Abstract]:Topological index is a very important research topic in chemical graph theory, and its research and development prospect is very extensive. It has important applications in the molecular structure of chemistry. In this paper, first, we give the calculation method of the first geometric arithmetic exponent about the graph, the whole graph and the subdivision graph; secondly, we give the first geometry arithmetic index about the graph. The extremum of total graph and subdivision graph and the corresponding polar graph problem. In the first chapter, the historical process of the study of the first geometry-arithmetic index is described, and some basic knowledge, relevant results and the main results in this paper are given. In the second chapter, we first give the calculation method of the first geometric arithmetic exponent about the graph, the whole graph and the subdivision graph, and by simplifying the first geometric arithmetic exponent online graph and the whole graph, we obtain the condition of the upper and lower bound of the first geometry arithmetic index graph and the whole graph. The exact values of the upper and lower bounds of the first geometric arithmetic exponent of the graph and the whole graph are obtained, and the corresponding polar graphs when the extremum is reached are described, and the extreme values of the upper and lower bounds of the first geometric arithmetic exponent in the subdivision graph are added. At the same time, we describe the corresponding pole diagram when the extremum is reached.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5

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