图的Laplacian矩阵谱半径  

The Spectral Radius of Laplacian Matrices of Graphs

作　　者：乔晓云[1] 

机构地区：[1]山西大学商务学院,山西太原030031

出　　处：《太原师范学院学报（自然科学版）》2014年第1期5-7,共3页Journal of Taiyuan Normal University:Natural Science Edition

基　　金：山西大学商务学院科研基金项目(LX2010036)

摘　　要：设G为n阶简单连通图,若L(G)为图G的度对角矩阵与邻接矩阵的差,则称L(G)为图G的Laplacian矩阵.结合非负矩阵谱理论,利用图的顶点度和平均二次度给出了图G的Laplacian矩阵的谱半径的新上界,同时给出了达到上界的极图.Let Gbe a simple and connected graph with n vertices,the matrix L（G）is called the Laplacian matrix of a graph G,if it is the difference between the diagonal matrix of vertex degrees and the adjacency matrix of G.The spectral theory of nonnegative matrices was used to present a new upper bound of Spectral Radius of Laplacian Matrices of graphs in terms of the vertex degree and the average 2-degree.Moreover,the extremal graph which achieves the upper bound was determined.

关 键 词：图 LAPLACIAN矩阵 非负矩阵 谱半径 上界 

分 类 号：O157.5[理学—数学]