On Laplacian eigenvalues of a graph

被引：16

作者：

Zhou, B ^{[1
]}

机构：

[1] S China Normal Univ, Dept Math, Guangzhou 510631, Peoples R China

来源：

ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES | 2004年 / 59卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Laplacian eigenvalue; line graph; bipartite graph;

D O I：

10.1515/zna-2004-0310

中图分类号：

O64 [物理化学（理论化学）、化学物理学];

学科分类号：

070304 ; 081704 ;

摘要：

Let G be a connected graph with n vertices and in edges. The Laplacian eigenvalues are denoted by mu(1) (G) greater than or equal to mu(2) (G) greater than or equal to(...)greater than or equal to mu(n-1) (G) > mu(n) (G) = 0. The Laplacian eigenvalues have important applications in theoretical chemistry. We present upper bounds for mu(1) (G) + (...) + mu(k) (G) and lower bounds for mu(n-1) (G) + (...) + mu(n-k) (G) in terms of n and m, where 1 less than or equal to k less than or equal to n-2, and characterize the extremal cases. We also discuss a type of upper bounds for mu(1) (G) in terms of degree and 2-degree.

引用

页码：181 / 184

页数：4

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