A sharp upper bound on the largest Laplacian eigenvalue of weighted graphs

被引：22
|
作者：
Das, KC [1 ]
Bapat, RB [1 ]
机构：
[1] Indian Stat Inst, New Delhi 110016, India
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2005年 / 409卷
关键词：
weighted graph; Laplacian matrix; largest eigenvalue; upper bound;
D O I：
10.1016/j.laa.2005.06.024
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider weighted graphs, where the edge weights are positive definite matrices. The Laplacian of the graph is defined in the usual way. We obtain an upper bound on the largest eigenvalue of the Laplacian and characterize graphs for which the bound is attained. The classical bound of Anderson and Morley, for the largest eigenvalue of the Laplacian of an unweighted graph follows as a special case. (c) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码：153 / 165
页数：13
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