由广义Bethe树和完全图所构造的图的谱(英文)  

The Spectrum of a Graph Obtained from Copies of a Generalized Bethe Tree and a Complete Graph

作　　者：何江宏[1] 范益政[1] 李双东[1] 

机构地区：[1]安徽大学数学科学学院,合肥230039

出　　处：《工程数学学报》2012年第5期763-772,共10页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11071002);the Program for NewCentury Excellent Talents in University,Key Project of Chinese Ministry of Education(210091);the Specialized Research Fund for the Doctoral Program of Higher Education(20103401110002);the Science andTechnological Fund of Anhui Province for Outstanding Youth(10040606Y33);the Project of Anhui Prov-ince for Excellent Young Talents in Universities(2009SQRZ017ZD);the Project of Educational Departmentof Anhui Province(KJ2010B136);the Scientific Research Fund for Fostering Distinguished Young Scholars of Anhui University(KJJQ1001);the Project for Academic Innovation Team of Anhui University(KJTD001B)

摘　　要：广义Bethe树是指每层上的点都具有相同度的带根树.设Bk为具有k层的广义Bethe树,Kr为r阶完全图.把r个Bk的根点分别粘在Kr的r个点上,可获得一个图BkoKr.借助于k阶对称三对角矩阵,本文给出邻接矩阵A(BkoKr)和Laplace矩阵L(BkoKr)的特征值的简洁刻画.此外,本文还给出了A(BkoKr)的Perron向量的结构性质.A generalized Bethe tree is a rooted tree for which the vertices in each level having equal degree. Let Вk be a generalized Bethe tree of k level, and let К^τ be a complete graph on r vertices. Then a graph В_κοК^τ is obtained from r copies ofВk and К^τ by appending r roots to the vertices of К^τ, respectively. In this paper, a simple way is introduced to characterize the eigenvalues of the adjacency matrix A（В_κοК^τ）and the Laplaeian matrix L（В_κοК^τ）of В_κοК^τ means of symmetric tridiagonal matrices of order k. In addition, the structure property of the Perron vectors of A（В_κοК^τ）is given.

关 键 词：Bethe树 LAPLACE矩阵 邻接矩阵 代数连通度 PERRON向量 

分 类 号：O157.5[理学—数学]