Upper Bounds for the Laplacian Graph Eigenvalues  

作　　者：JiongShengLI YongLiangPAN 

机构地区：[1]DepartmentofMathematics,UniversityofScienceandTechnologyofChina,Hefei230026,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2004年第5期803-806,共4页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.19971086)

摘　　要：We first apply non-negative matrix theory to the matrix K=D+A,where D and A are the degree-diagonal and adjacency matrices of a graph G,respectively,to establish a relation on the largest Laplacian eigenvalue λ_1(G)of G and the spectral radius ρ(K)of K.And then by using this relation we present two upper bounds for λ_1(G)and determine the extremal graphs which achieve the upper bounds.We first apply non-negative matrix theory to the matrix K=D+A,where D and A are the degree-diagonal and adjacency matrices of a graph G,respectively,to establish a relation on the largest Laplacian eigenvalue λ_1(G)of G and the spectral radius ρ(K)of K.And then by using this relation we present two upper bounds for λ_1(G)and determine the extremal graphs which achieve the upper bounds.

关 键 词：GRAPH Laplacian matrix Largest eigenvalue Upper bound 

分 类 号：O157.5[理学—数学]