Eigenvalues of graphs and a simple proof of a theorem of Greenberg

被引：9

作者：

Cioaba, Sebastian M. ^{[1
]}

机构：

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

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2006年 / 416卷 / 2-3期

关键词：

spectral radius; universal cover; eigenvalues;

D O I：

10.1016/j.laa.2005.12.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In his Ph.D. thesis, Greenberg proved that if p(5) is the spectral radius of the universal cover 5 of a finite graph X, then for each epsilon > 0, a positive proportion (depending only on (X) over tilde and epsilon) of the eigenvalues of X have absolute value at least p ((X) over tilde) - epsilon. In this paper, we show that the same result holds true if we remove absolute from the previous result. We also prove an analogue result for the smallest eigenvalues of X. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：776 / 782

页数：7

共 50 条

[21] A simple proof of the alternation theorem
Vaidyanathan, P. P.
Nguyen, T. Q.
CONFERENCE RECORD OF THE FORTY-FIRST ASILOMAR CONFERENCE ON SIGNALS, SYSTEMS & COMPUTERS, VOLS 1-5, 2007, : 1111 - +
[22] A simple proof of a theorem of Schur
Mirzakhani, M
AMERICAN MATHEMATICAL MONTHLY, 1998, 105 (03): : 260 - 262
[23] A simple proof of a theorem of Milner
Katona, GOH
JOURNAL OF COMBINATORIAL THEORY SERIES A, 1998, 83 (01) : 138 - 140
[24] A simple proof of the FWL theorem
Lovell, Michael C.
JOURNAL OF ECONOMIC EDUCATION, 2008, 39 (01): : 88 - 91
[25] SIMPLE PROOF OF KASINS THEOREM
TANDORI, K
ACTA SCIENTIARUM MATHEMATICARUM, 1977, 39 (1-2): : 175 - 178
[26] A SIMPLE PROOF OF KHARITONOV THEOREM
YEUNG, KS
WANG, SS
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1987, 32 (09) : 822 - 823
[27] A SIMPLE PROOF OF A THEOREM OF JUNG
BAUER, D
MORGANA, A
SCHMEICHEL, EF
DISCRETE MATHEMATICS, 1990, 79 (02) : 147 - 152
[28] A SIMPLE PROOF OF A THEOREM OF ISBELL
KRUSE, A
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 18 (03) : 546 - +
[29] SIMPLE PROOF OF SIEGELS THEOREM
GOLDFELD, DM
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1974, 71 (04) : 1055 - 1055
[30] SIMPLE PROOF OF A THEOREM ON PERMANENTS
DJOKOVIC, DZ
GLASGOW MATHEMATICAL JOURNAL, 1969, 10 : 52 - &

← 1 2 3 4 5 →