本文選題：拉普拉斯矩陣特征值 + 基爾霍夫指標(biāo)��； 參考：《廣東技術(shù)師范學(xué)院》2017年碩士論文

【摘要】：在本文中,主要討論圖的拉普拉斯矩陣特征值的兩個(gè)相關(guān)指標(biāo):基爾霍夫指標(biāo)(Kf)和擬拉普拉斯能量不變量(LEL).由于基爾霍夫指標(biāo)與擬拉普拉斯能量在數(shù)學(xué)方面難以計(jì)算,所以我們一般研究基爾霍夫指標(biāo)與擬拉普拉斯能量的界并且研究圖類中基爾霍夫指標(biāo)和擬拉普拉斯能量的比較,由數(shù)學(xué)的不等式可以清楚地呈現(xiàn)出圖的性質(zhì)與圖的結(jié)構(gòu);而從圖的結(jié)構(gòu)也可以歸納出不等式.對(duì)于基爾霍夫指標(biāo)與擬拉普拉斯能量的比較,已經(jīng)有大量的文獻(xiàn)[10,15,35,36].本文致力解決這兩種的問題.本文取得的主要工作可概括如下:1.第二章中,通過基爾霍夫指標(biāo)和擬拉普拉斯能量的計(jì)算,比較得到與最大度有關(guān)的不等式,則有LEL(G)(27)Kf(G).2.第三章,由剖分圖是二部圖,得出剖分圖都是LEL(S(G))(27)Kf(S(G));3.第四章,我們給出了全部化學(xué)圖的基爾霍夫指標(biāo)和擬拉普拉斯能量的比較;4.第五章,證明正則圖與其線圖的基爾霍夫指標(biāo)和擬拉普拉斯能量的比較;5.第六章,給定點(diǎn)數(shù)和圈數(shù)的基爾霍夫指標(biāo)和擬拉普拉斯能量的比較.通過圖的拓?fù)渲笜?biāo),給出特定范圍的基爾霍夫指標(biāo)和擬拉普拉斯能量的比較.再用Mathmatica和New Graph軟件計(jì)算出有限個(gè)圖的基爾霍夫指標(biāo)和擬拉普拉斯能量,這樣,我們就可以得出基爾霍夫指標(biāo)和擬拉普拉斯能量的比較.
[Abstract]:In this paper, we mainly discuss two related indexes of Laplace matrix eigenvalue of graphs: Kirchhoff index (Kf) and quasi-Laplace energy invariant (LEL). Since it is difficult to calculate the Kirchhoff index and the quasi-Laplacian energy in mathematics, we generally study the bounds of the Kirchhoff index and the quasi-Laplacian energy and study the comparison between the Kirchhoff index and the quasi-Laplacian energy in the graph class. The properties and structure of graphs can be clearly shown by mathematical inequalities, and inequalities can also be induced from the structure of graphs. For the comparison of Kirchhoff index and quasi-Laplacian energy, there are a lot of references [10 / 15 / 3536]. This paper is devoted to solving these two kinds of problems. The main work of this paper can be summarized as follows: 1. In the second chapter, through the Kirchhoff index and the calculation of quasi-Laplacian energy, the inequality related to maximum degree is obtained, and there are les (G) (27) Kf (G) .2. In chapter 3, from the bipartite graph, it is obtained that the partition graph is all L (S (G) (27) K f (S (G) F (S (G) 3. In chapter 4, we give the Kirchhoff index of all chemical graphs and the comparison of quasi-Laplace energy. In chapter 5, we prove the comparison of Kirchhoff index and quasi-Laplace energy between regular graphs and their graphs. In chapter 6, the Kirchhoff index and quasi-Laplace energy of given number of points and cycles are compared. The comparison of Kirchhoff index and quasi-Laplace energy is given by topological index of graph. Then we use Mathmatica and New Graph software to calculate the Kirchhoff index and quasi-Laplace energy of finite graphs, so we can get the comparison of Kirchhoff index and quasi-Laplace energy.
【學(xué)位授予單位】：廣東技術(shù)師范學(xué)院
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O157.5
，

本文編號(hào)：2064394