图的基尔霍夫指标与拟拉普拉斯能量的比较

发布时间：2018-06-25 03:40

  本文选题：拉普拉斯矩阵特征值 + 基尔霍夫指标　； 参考：《广东技术师范学院》2017年硕士论文

【摘要】：在本文中,主要讨论图的拉普拉斯矩阵特征值的两个相关指标:基尔霍夫指标(Kf)和拟拉普拉斯能量不变量(LEL).由于基尔霍夫指标与拟拉普拉斯能量在数学方面难以计算,所以我们一般研究基尔霍夫指标与拟拉普拉斯能量的界并且研究图类中基尔霍夫指标和拟拉普拉斯能量的比较,由数学的不等式可以清楚地呈现出图的性质与图的结构;而从图的结构也可以归纳出不等式.对于基尔霍夫指标与拟拉普拉斯能量的比较,已经有大量的文献[10,15,35,36].本文致力解决这两种的问题.本文取得的主要工作可概括如下:1.第二章中,通过基尔霍夫指标和拟拉普拉斯能量的计算,比较得到与最大度有关的不等式,则有LEL(G)(27)Kf(G).2.第三章,由剖分图是二部图,得出剖分图都是LEL(S(G))(27)Kf(S(G));3.第四章,我们给出了全部化学图的基尔霍夫指标和拟拉普拉斯能量的比较;4.第五章,证明正则图与其线图的基尔霍夫指标和拟拉普拉斯能量的比较;5.第六章,给定点数和圈数的基尔霍夫指标和拟拉普拉斯能量的比较.通过图的拓扑指标,给出特定范围的基尔霍夫指标和拟拉普拉斯能量的比较.再用Mathmatica和New Graph软件计算出有限个图的基尔霍夫指标和拟拉普拉斯能量,这样,我们就可以得出基尔霍夫指标和拟拉普拉斯能量的比较.
[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.
【学位授予单位】：广东技术师范学院
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5
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本文编号：2064394