On the second Laplacian eigenvalues of trees of odd order
type: Item
instance of: scholarly article
title: On the second Laplacian eigenvalues of trees of odd order
zbMATH Open document ID: 1110.05063
author: Li Zhang
author: Xiying Yuan
author: Jia-Yu Shao
published in: Linear Algebra and its Applications
publication date: 2007-02-14T00:00:00Z
review text: In the paper, the second Laplacian eigenvalue of a tree \(T\), \(\lambda_2(T)\), is studied. It is shown that among all trees of odd order \(2t+1\) (\(t\geq 4\)) the largest value of \(\lambda_2(T)\) is \(\frac 12(t+1+\sqrt{t^2+2t-3})\), while the second largest value of \(\lambda_2(T)\) is the second largest root of the cubic equation \(x^3-(2t+3)x^2+(t^2+3t+3)x-(2t+1)=0\). Trees for which these bounds are attained are constructed.
reviewed by: Martin Knor
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 5126022
MaRDI profile type: Publication
full work available at URL: j.laa.2006.05.021
OpenAlex ID: W1976500712
cites work: Bounds on the \(k\)th eigenvalues of trees and forests
cites work: Ordering trees by algebraic connectivity
cites work: On the second largest Laplacian eigenvalue of trees
cites work: Q4710059
cites work: A new upper bound for eigenvalues of the Laplacian matrix of a graph
DOI: 10.1016/J.LAA.2006.05.021
description: scientific article; zbMATH DE number 5126022