Sharp lower bounds on the eigenvalues of trees
type: Item
instance of: scholarly article
title: Sharp lower bounds on the eigenvalues of trees
zbMATH Open document ID: 0677.05058
DOI: 10.1016/0024-3795(89)90288-7
author: Hong Yuan
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: It is proved that the smallest positive eigenvalue in a forest with n vertices is bounded from below by the same eigenvalue in a path with \(2\lfloor n/2\rfloor\) vertices. With some exceptions (which are described), the second largest eigenvalue of a tree is not smaller than 1.
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 4108820
zbMATH Keywords: eigenvalue
zbMATH Keywords: forest
reviewed by: Dragoš Cvetković
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90288-7
OpenAlex ID: W2013867978
cites work: Q3907599
cites work: Inverses of trees
description: scientific article; zbMATH DE number 4108820