Extreme eigenvalues of nonregular graphs

被引：38

作者：

Cioaba, Sebastian M. ^{[1
]}

Gregory, David A.

Nikiforov, Vladimir

机构：

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[2] Queens Univ, Dept Math, Kingston, ON K7L 3N6, Canada

[3] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES B | 2007年 / 97卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

spectral radius; nonregular graph; eigenvalues;

D O I：

10.1016/j.jctb.2006.07.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let lambda(1) be the greatest eigenvalue and lambda(n) the least eigenvalue of the adjacency matrix of a connected graph G with n vertices, m edges and diameter D. We prove that if G is nonregular, then [GRAPH] where A is the maximum degree of G. The inequality improves previous bounds of Stevanovic and of Zhang. It also implies that a lower bound on lambda(n) obtained by Alon and Sudakov for (possibly regular) connected nonbipartite graphs also holds for connected nonregular graphs. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：483 / 486

页数：4