三类图的拉普拉斯谱半径的极限点  

Limit Points of Laplacian Spectral Radii of Three Types of Graphs

作　　者：李静花 何常香[1] LI Jinghua;HE Changxiang(College of Science, University of Shanghai for Science and Technology, Shanghai 200093, Chin)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2018年第2期121-126,共6页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学基金资助项目(11301340;11201303);上海市自然科学基金资助项目(12ZR1420300);沪江基金资助项目(B14005)

摘　　要：将图的结构与对应的拉普拉斯矩阵相结合,研究其拉普拉斯特征多项式。根据拉普拉斯特征多项式的特征求出了图的拉普拉斯谱半径的极限点。利用图经粘连运算后的拉普拉斯特征多项式以及图的拉普拉斯谱半径的上界和下界,证明了三类图的拉普拉斯谱半径的极限点的存在性,证明了n→∞时图类的拉普拉斯谱半径是某方程的最大根。The Laplacian characteristic polynomials of the structures of graphs combined with corresponding Laplace matrices were studied. The limit points of the Laplacian spectral radii were provided according to the properties of Laplacian characteristic polynomials. For three types of graphs,the existence of limit points of the Laplacian spectral radii was proved and it was determined when n→∞, the Laplacian spectral radius of a graph is the largest root of certain equation by using some Laplacian characteristic polynomials of the graphs after coalescent operations and considering the upper and lower bounds of Laplacian spectral radii of the graphs.

关 键 词：拉普拉斯谱半径 极限点 粘连 

分 类 号：O157.5[理学—数学]