路矩阵相关谱半径和路谱展的界及其应用  

Bounds of correlation spectrum radius of path matrix and path spectrum spread and their applications

作　　者：卢鹏丽[1] 栾睿 LU Pengli;LUAN Rui(School of Computer and Communication,Lanzhou University of Technology,Lanzhou 730050,China)

机构地区：[1]兰州理工大学计算机与通信学院,甘肃兰州730050

出　　处：《哈尔滨工程大学学报》2023年第2期251-256,共6页Journal of Harbin Engineering University

基　　金：国家自然科学基金项目(11861045,62162040)。

摘　　要：由于图谱能够很好地反映图的结构性质且便于计算,本文通过图的矩阵,建立图谱与图的拓扑性质之间的联系,更好地反应图的结构和研究图的相关性质;利用矩阵论和图论的理论和方法,证明路谱半径的下界和路无符号拉普拉斯谱半径的上下界;定义路谱展并得到其上下界;最后作为应用,研究完全r-部图的路谱、路拉普拉斯谱和路无符号拉普拉斯谱并得到了图K_(p,p,…,p)的相关能量。The graph spectrum can well reflect the structural properties of graphs and is easy to calculate.In this paper,the relationship between graph spectrum and topological properties of graph is established by the matrix of graph,so as to better reflect the structure of graph and study related properties of the graph.Using the theory and method of matrix theory and graph theory,we prove the lower bound of the path spectrum radius and the upper and lower bounds of the path signless Laplacian spectrum radius.We define the path spectrum spread and get the upper and lower bounds.Finally,as an application,we study the complete r-partite graph,get the path spectrum,path Laplacian spectrum and path signless Laplacian spectrum and related energy of K_(p,p,…,p).

关 键 词：路矩阵 路谱展 路谱半径 能量 路无符号拉普拉斯谱半径 完全r-部图 路谱 路(无符号)拉普拉斯谱 

分 类 号：O157.5[理学—数学] O157.6[理学—基础数学]