A sharp upper bound on the largest eigenvalue of the Laplacian matrix of a graph

被引：52
|
作者：
Shu, JL [1 ]
Hong, Y [1 ]
Wen-Ren, K [1 ]
机构：
[1] E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2002年 / 347卷 / 1-3期
基金：
中国国家自然科学基金;
关键词：
line graph; degree sequence; adjacency spectral radius; Laplacian spectral radius;
D O I：
10.1016/S0024-3795(01)00548-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let G be a simple connected graph with it vertices. The largest eigenvalue of the Laplacian matrix of G is denoted by V (G). Suppose the degree sequence of G is d(1) greater than or equal to d(2) greater than or equal to ...greater than or equal tod(n). In this paper, we present a sharp upper bound of mu (G) mu(G) less than or equal to d(n) + 1/2 + root(d(n) - 1/2)(2) + Sigma(i=1)(n) d(i)(d(i) - d(n)), the equality holds if and only if G is a regular bipartite graph. (C) 2002 Published by Elsevier Science Inc.
引用
收藏
页码：123 / 129
页数：7
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