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Bounds of eigenvalues of a graph

Bounds of eigenvalues of a graph LetG be a simple graph withn vertices. We denote by λi(G) thei-th largest eigenvalue ofG. In this paper, several results are presented concerning bounds on the eigenvalues ofG. In particular, it is shown that −1⩽λ2(G)⩽(n−2)/2, and the left hand equality holds if and only ifG is a complete graph with at least two vertices; the right hand equality holds if and only ifn is even andG℞2K n/2. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Bounds of eigenvalues of a graph

Acta Mathematicae Applicatae Sinica , Volume 4 (2) – Jul 13, 2005

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References (9)

Publisher
Springer Journals
Copyright
Copyright © 1988 by Science Press, Beijing, China and Allerton Press, Inc. New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02006065
Publisher site
See Article on Publisher Site

Abstract

LetG be a simple graph withn vertices. We denote by λi(G) thei-th largest eigenvalue ofG. In this paper, several results are presented concerning bounds on the eigenvalues ofG. In particular, it is shown that −1⩽λ2(G)⩽(n−2)/2, and the left hand equality holds if and only ifG is a complete graph with at least two vertices; the right hand equality holds if and only ifn is even andG℞2K n/2.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

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