本文選題：度距離 + Newkome樹狀大分子圖　； 參考：《大連海事大學(xué)》2017年碩士論文

【摘要】：度距離是圖中頂點(diǎn)度和距離相關(guān)的一類參數(shù),是Wiener指標(biāo)的一個(gè)變體,它反映了大分子有機(jī)物某些物理化學(xué)性質(zhì).自1994年,由Dobrynin,Kochetova和Gutman首次提出以來,關(guān)于圖的度距離、度距離極圖、圖的頂點(diǎn)度距離及極值問題得到了廣泛關(guān)注.本文針對(duì)三類圖結(jié)構(gòu)——Newkome樹狀大分子圖、六元素環(huán)螺鏈圖和擴(kuò)展雙星樹的(頂點(diǎn))度距離及度距離排序問題開展研究,主要工作和成果如下:(1)基于Newkome樹枝醇結(jié)構(gòu),定義了 一種類Newkome樹枝醇結(jié)構(gòu)的樹—-Newkome樹狀大分子圖.根據(jù)Newkome樹狀大分子圖的"遞歸"結(jié)構(gòu),給出了該圖的一種分解方法,并采用遞歸方法研究了該圖的頂點(diǎn)度距離,得到了頂點(diǎn)度距離的顯性表達(dá)式及Newkome樹狀大分子圖的度距離.(2)對(duì)于六元素環(huán)螺鏈圖類的兩種特殊結(jié)構(gòu)——2位-六元素環(huán)螺鏈圖和3位-六元素環(huán)螺鏈圖,根據(jù)其結(jié)構(gòu)的"螺接性"和"螺解性",采用遞歸方法了研究2位和3位兩類六元素環(huán)螺鏈圖的頂點(diǎn)度距離,得到了任意頂點(diǎn)的頂點(diǎn)度距離的顯性表達(dá)式及圖的度距離.(3)對(duì)擴(kuò)展雙星樹的頂點(diǎn)度距離進(jìn)行了研究,給出了圖中頂點(diǎn)的頂點(diǎn)度距離值的排序,證明了度距離最大值點(diǎn)為多懸掛點(diǎn)的星心、星心間路上頂點(diǎn)的頂點(diǎn)度距離值具有下凹性.
[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.

【學(xué)位授予單位】：大連海事大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O157.5

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相關(guān)期刊論文 前5條

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本文編號(hào)：1834223