本文選題：拓撲指數(shù) + 第一幾何-算數(shù)指數(shù)　； 參考：《中北大學(xué)》2017年碩士論文

【摘要】：拓撲指數(shù)是化學(xué)圖論中一個非常重要的研究課題,其研究和發(fā)展前景非常廣泛.它在化學(xué)的分子結(jié)構(gòu)中有重要的應(yīng)用.在這篇文章中,首先,我們給出了第一幾何-算數(shù)指數(shù)關(guān)于線圖、全圖和細分圖的計算方法;其次,我們給出了第一幾何-算數(shù)指數(shù)關(guān)于線圖、全圖和細分圖的極值及其對應(yīng)的極圖問題.在第一章中,講了第一幾何-算數(shù)指數(shù)研究的歷史過程,給出了一些基本的知識、相關(guān)的結(jié)果及此文的主要結(jié)果.在第二章中,首先給出了第一幾何-算數(shù)指數(shù)關(guān)于線圖、全圖和細分圖的計算方法;通過簡化第一幾何-算數(shù)指數(shù)在線圖和全圖達到上下界的條件,得到了線圖和全圖其第一幾何-算數(shù)指數(shù)上下界的精確值,且刻畫了達到極值時相應(yīng)的極圖;補充了第一幾何-算數(shù)指數(shù)在細分圖中上下界的極值,且刻畫了達到極值時相應(yīng)的極圖.
[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.
【學(xué)位授予單位】：中北大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O157.5

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