图的原子键连通性指数

发布时间：2018-05-10 13:58

本文选题：ABC指数 + ABC_(GG)指数　；参考：《五邑大学》2017年硕士论文

【摘要】：本文研究了图的ABC指数和两类广义ABC指数,即ABC_(GG)指数和ABC_3指数.利用图变换、某些特殊二元函数的性质和数论相关的理论,并结合已有的研究方法,确定了上述指数的若干极值,并刻画了相关的极图.第一章给出了与本研究相关的图论的基本知识,包括图的基本概念和术语,若干拓扑指标的相关背景,以及本文的主要结果.第二章确定了图的直积、析取和对称差的ABC指数的上界,以及图的联、笛卡尔乘积和冠状乘积的ABC_(GG)指数的上界,证明了这些上界都是紧的,并且刻画了对应的极图,主要结论见定理2.1.1、2.1.2、2.1.3、2.2.1、2.2.2和2.2.3.第三章确定了双圈图的最大ABC_(GG)指数,并刻画了对应的极图,主要结论见定理3.2.9.第四章确定了分别给定围长和阶数的单圈图的最大、次大ABC_3指数,以及分别给定直径和阶数的树的最大、次大ABC_3指数,主要结论见定理4.2.3、4.3.3和定理4.4.2,并刻画了对应的极图。
[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.
【学位授予单位】：五邑大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5

【参考文献】