本文選題：特殊圖　切入點(diǎn)：拉普拉斯能量　出處：《大連海事大學(xué)》2017年碩士論文

【摘要】：著名的格尼斯堡七橋問題是圖論問題的起源,隨后圖論便成為應(yīng)用數(shù)學(xué)研究中的一個(gè)重要分支。圖的Laplacian能量問題是圖論研究領(lǐng)域的熱點(diǎn)問題,最初是由Ivan Gutman、Bo Zhou等人將其概念引入到文獻(xiàn)中的。它不僅具有理論價(jià)值,更具有重要的實(shí)際價(jià)值。圖的Laplacian能量廣泛應(yīng)用于量子化學(xué)、圖像層次體系分割、計(jì)算機(jī)科學(xué)等領(lǐng)域。令G= V E)為一個(gè)非平凡連通圖,邊集為E(G),其邊數(shù)為m,頂點(diǎn)集為V(G),其頂點(diǎn)數(shù)為n。若用A(G)表示圖G的鄰接矩陣,用D(G)表示圖G的點(diǎn)的度矩陣,則L(G)=D(G)-A(G)即為圖的 Laplacian 矩陣,可以用μi(i=1,2,3...n)表示圖的 Laplacian特征值,且μ1≥μ2≥ …μn= 0。則圖的Laplacian能量的公式記為LE(G)=∑i=1 n |μi-2m/n|.本文研究了一些應(yīng)用廣泛的特殊圖的Laplacian能量的問題,結(jié)構(gòu)及其結(jié)果如下:(1)介紹了圖論的背景及圖的Laplacian能量的基本概念和已有的結(jié)論;基于矩陣特征值計(jì)算方法,得到了完全圖的刺圖的Laplacian能量的上下界。(2)利用數(shù)學(xué)歸納法、分類討論思想,得到了圈的并圖、風(fēng)車圖的Laplacian能量的表達(dá)式及其上下界。(3)利用數(shù)學(xué)歸納法、計(jì)算機(jī)語言創(chuàng)新序列表示方法、分類討論、最優(yōu)化思想,得到了 k-tree 的 Laplacian 能量與 Laplacian 特征值。
[Abstract]:The famous Gneisburg Seven Bridge problem is the origin of graph theory, and then graph theory becomes an important branch of applied mathematics.The Laplacian energy problem of graphs is a hot topic in the field of graph theory, which was first introduced into the literature by Ivan Gutman and Bo Zhou et al.It not only has theoretical value, but also has important practical value.The Laplacian energy of graphs is widely used in quantum chemistry, image hierarchical system segmentation, computer science and so on.Let G = V E) be a nontrivial connected graph, the edge set is an En G ~ (1), the number of edges is m, the vertex set is V _ n G ~ (1), and the number of vertices is n.If the adjoining matrix of graph G is expressed by Agng and the degree matrix of the point of graph G is denoted by DG, then the Laplacian matrix of the graph is the Laplacian matrix of the graph, and the Laplacian eigenvalue of the graph can be expressed by 渭 ~ (1) I ~ (1) (渭 _ (1) 鈮，

本文編號(hào)：1715454