几类图的度距离研究

发布时间：2018-05-02 14:06

本文选题：度距离 + Newkome树状大分子图　；参考：《大连海事大学》2017年硕士论文

【摘要】：度距离是图中顶点度和距离相关的一类参数,是Wiener指标的一个变体,它反映了大分子有机物某些物理化学性质.自1994年,由Dobrynin,Kochetova和Gutman首次提出以来,关于图的度距离、度距离极图、图的顶点度距离及极值问题得到了广泛关注.本文针对三类图结构——Newkome树状大分子图、六元素环螺链图和扩展双星树的(顶点)度距离及度距离排序问题开展研究,主要工作和成果如下:(1)基于Newkome树枝醇结构,定义了一种类Newkome树枝醇结构的树—-Newkome树状大分子图.根据Newkome树状大分子图的"递归"结构,给出了该图的一种分解方法,并采用递归方法研究了该图的顶点度距离,得到了顶点度距离的显性表达式及Newkome树状大分子图的度距离.(2)对于六元素环螺链图类的两种特殊结构——2位-六元素环螺链图和3位-六元素环螺链图,根据其结构的"螺接性"和"螺解性",采用递归方法了研究2位和3位两类六元素环螺链图的顶点度距离,得到了任意顶点的顶点度距离的显性表达式及图的度距离.(3)对扩展双星树的顶点度距离进行了研究,给出了图中顶点的顶点度距离值的排序,证明了度距离最大值点为多悬挂点的星心、星心间路上顶点的顶点度距离值具有下凹性.
[Abstract]:Degree distance is a class of parameters related to vertex degree and distance in a graph. It is a variant of the Wiener index. It reflects some physical and chemical properties of macromolecular organic matter. Since 1994, the degree distance, degree distance polar map, vertex distance and extreme value of graphs have been paid much attention to since first proposed by Dobrynin, Kochetova and Gutman. The main work and results are as follows: (1) a tree - -Newkome tree - like map of Newkome dendrol structure based on Newkome dendrol structure is defined as follows: Newkome tree like macromolecular graph, six element ring snails graph and extended binary tree (vertex) degree distance and degree distance sorting problem. Newkome tree like macromolecular graph "recursion" structure, gives a method of decomposition of the graph, and uses the recursive method to study the vertex degree distance of the graph, obtains the explicit expression of vertex degree distance and the degree distance of the Newkome tree like macromolecule graph. (2) the two special structures of the six element ring snails map class, 2 bit and six element ring snails Chain graph and 3 - six element ring snails chart, based on the "snails" and "snails" of its structure, use recursive method to study the vertex distance of the 2 and 3 two class six element ring snails graph, get the explicit expression of the vertex degree distance of any vertex and the degree distance of the graph. (3) the distance of the vertex degree of the extended binary tree is studied. By sorting the vertex degree distance of the vertex of the graph, it is proved that the maximum point of the degree distance is the star center of the multi suspension point, and the vertex degree distance of the vertex between the stars in the star center is concave.

【学位授予单位】：大连海事大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5

【参考文献】