K阶连通指标论文：图论中一些拓扑指标研究.doc

K阶连通指标论文：图论中一些拓扑指标研究【中文摘要】本文主要将一些图论中拓扑指标(如Randic指标、Zagreb指标、K阶连通指标等)的已有结果做了一些推广,得到了更加一般的结果。第一章介绍了图论及相关拓扑指标的一些基本知识。第二章至第五章为本文的主要结果。其中第二章将一簇无限树枝状化合物(dendrimer nanostars)图的2阶连通指标结果推广到了该类图的K阶连通指标。第三章将给定最大度、第二最大度及最小度连通图Zagreb指标的上界结果推广到给定若干最大度及若干最小度连通图的Zagreb指标的上界。第四章将烷烃分子图(度数不大于4的简单连通图)Randic指标的上下界结果推广到度数不大于给定的值?,不小于给定的值的简单连通图的Randic指标的上下界。第五章将分子图(度数不大于4的简单连通图)零阶广义Randic指标的上下界结果推广到度数不大于给定的值?,不小于给定的值的简单连通图的零阶广义Randic指标的上下界,并构造了取到上下界的极值图。【英文摘要】In this dissertation, we mainly develop some results of topology indices, suchas Randic index, Zagreb index, K-connectivity index, etc. and get some moregeneral results. The ?rst chapter introduces some basic knowledge of graph theoryand related topology indices. Chapter II to Chapter V are the main results of thedissertation. In chapter II we develop the K-connectivity index of an in?nite classof dendrimer nanostars from the result of the second-connectivity index of suchgraph. In chapter III we develop the upper bound of Zagreb indices when givenseveral maximum and minimum degrees from from the result of the upper boundof Zagreb indices when given the maximum, second maximum and the minimumdegrees. In chapter IV we develop the upper bound and the lower bound of Randicindex of a connected graph when the maximum degree is not greater than ? andthe minimum degree is not less thanfrom the result of the upper bound and thelower bound of Randic index of an alkane graph(the connected graph which themaximum degree is not greater than 4). In chapter V we develop the upper boundand the lower bound of zeroth-order general Randic index of a connected graphwhen the maximum degree is not greater than ? and the minimum degree is notless thanfrom the result of the upper bound and the lower bound of zeroth-order general Randic index of a morecular graph(the connected graph which themaximum degree is not greater than 4), and construct extremal graphs to attainthe upper and lower bound.【备注】索购全文在线加好友：1.3.9.9.3.8848 同时提供论文写作一对一指导和论文发表委托服务【关键词】K阶连通指标 Zagreb指标 Randic指标 零阶广义Randic指标 最大度 最小度【英文关键词】K-connectivity index Zagreb index Randic index zeroth-order gen-eral Randic index maximum degree minimum degree【目录】图论中一些拓扑指标研究摘要4-5ABSTRACT5第一章 引言8-141.1 图论概述81.2 图的基本概念8-91.3 分子图与分子拓扑指标的应用9-101.4 Randic指标及与其它拓扑指标定义10-111.5 本文的研究方向与主要结论11-14第二章 K 阶连通指标14-242.1 相关介绍14-152.2 主要研究成果15-24第三章 Zagreb 指标24-383.1 相关介绍243.2 主要研究成果24-38第