The minimum number of multiplicity 1 eigenvalues among real symmetric matrices whose graph is a nonlinear tree
type: Item
instance of: scholarly article
title: The minimum number of multiplicity 1 eigenvalues among real symmetric matrices whose graph is a nonlinear tree
zbMATH Open document ID: 1489.15017
author: Yanyan Li
published in: Special Matrices
publication date: 2022-02-18T00:00:00Z
review text: Let \(T\) be a nonlinear tree, that is, a tree without a path with all its vertices of degree greater than two. Let \(\mathcal{S}(T)\) be the set of the symmetric matrices associated with \(T\). This paper deals with the minimum number of eigenvalues with multiplicity one for \(A\in\mathcal{S}(T)\). This number is denoted by \(U(T)\). In Section 3 the authors study the nonlinear trees using the diameter. Section 4, the most important section of this paper, contains the main results about the number \(U(T)\). Theorems 4.2 and 4.3 show that \(U(T)=2\) when \(T\) has diameter 5 or 6. In this section there are also two conjectures (Conjectures 4.9 and 4.13). In my opinion, the results of this paper will help new researchers to solve this challenging problem.
reviewed by: Rosário Fernandes
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 7476482
zbMATH Keywords: eigenvalue
zbMATH Keywords: graph of a matrix
zbMATH Keywords: multiplicity list
zbMATH Keywords: nonlinear tree
describes a project that uses: OEIS
MaRDI profile type: Publication
full work available at URL: spma-2021-0158
OpenAlex ID: W4210768082
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DOI: 10.1515/SPMA-2021-0158
description: scientific article; zbMATH DE number 7476482