本文選題：ABC指數(shù) + ABC_(GG)指數(shù)��； 參考：《五邑大學(xué)》2017年碩士論文

【摘要】：本文研究了圖的ABC指數(shù)和兩類廣義ABC指數(shù),即ABC_(GG)指數(shù)和ABC_3指數(shù).利用圖變換、某些特殊二元函數(shù)的性質(zhì)和數(shù)論相關(guān)的理論,并結(jié)合已有的研究方法,確定了上述指數(shù)的若干極值,并刻畫了相關(guān)的極圖.第一章給出了與本研究相關(guān)的圖論的基本知識,包括圖的基本概念和術(shù)語,若干拓?fù)渲笜?biāo)的相關(guān)背景,以及本文的主要結(jié)果.第二章確定了圖的直積、析取和對稱差的ABC指數(shù)的上界,以及圖的聯(lián)、笛卡爾乘積和冠狀乘積的ABC_(GG)指數(shù)的上界,證明了這些上界都是緊的,并且刻畫了對應(yīng)的極圖,主要結(jié)論見定理2.1.1、2.1.2、2.1.3、2.2.1、2.2.2和2.2.3.第三章確定了雙圈圖的最大ABC_(GG)指數(shù),并刻畫了對應(yīng)的極圖,主要結(jié)論見定理3.2.9.第四章確定了分別給定圍長和階數(shù)的單圈圖的最大、次大ABC_3指數(shù),以及分別給定直徑和階數(shù)的樹的最大、次大ABC_3指數(shù),主要結(jié)論見定理4.2.3、4.3.3和定理4.4.2,并刻畫了對應(yīng)的極圖。
[Abstract]:In this paper, we study the ABC exponents of graphs and two classes of generalized ABC exponents, that is, the ABC_3 exponents and the ABC exponents. By means of graph transformation, the properties of some special binary functions and the related theory of number theory, and combining with the existing research methods, we determine some extreme values of the above exponents, and characterize the related polar graphs. The first chapter gives the basic knowledge of graph theory related to this study, including the basic concepts and terms of graphs, the relevant background of some topological indexes, and the main results of this paper. In the second chapter, we determine the upper bounds of the ABC exponent for the direct product, disjunction and symmetry difference of graphs, and the upper bounds for the ABC exponent of graph, Cartesian product and coronal product. It is proved that these upper bounds are compact, and the corresponding polar graphs are characterized. For the main conclusions, see Theorems 2.1.1 / 2.1.2 / 2.1.3 / 2.2.1.1 / 2.2.2.2 and 2.2.3. In chapter 3, we determine the maximum ABC _ S _ G _ G index of bicyclic graphs, and characterize the corresponding polar graphs. The main results are shown in Theorem 3.2.9. In chapter 4, we determine the maximum, sub-large ABC_3 exponent of a unicyclic graph with given girth and order, and the maximal and sub-large ABC_3 exponent of a tree with given diameter and order respectively. The main results are shown in Theorem 4.2.3 ~ 4.3.3 and Theorem 4.4.2, and the corresponding polar graphs are characterized.
【學(xué)位授予單位】：五邑大學(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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相關(guān)期刊論文 前1條

1 湯自凱;侯耀平;;關(guān)于第二原子鍵連通指數(shù)（英文）[J];湖南師范大學(xué)自然科學(xué)學(xué)報;2015年04期

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本文編號：1869589