DSpace
 
  Repositório Institucional da Universidade de Aveiro > Departamento de Matemática > MAT - Artigos >
 On the spectra of some graphs like weighted rooted trees
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/4282

title: On the spectra of some graphs like weighted rooted trees
authors: Fernandes, R.
Gomes, H.
Martins, E.A.
keywords: Adjacency matrix
Eigenvalues
Graph
Laplacian matrix
issue date: 2008
publisher: Elsevier
abstract: Let G be a weighted rooted graph of k levels such that, for j ∈ {2, ..., k}(1)each vertex at level j is adjacent to one vertex at level j - 1 and all edges joining a vertex at level j with a vertex at level j - 1 have the same weight, where the weight is a positive real number;(2)if two vertices at level j are adjacent then they are adjacent to the same vertex at level j - 1 and all edges joining two vertices at level j have the same weight;(3)two vertices at level j have the same degree;(4)there is not a vertex at level j adjacent to others two vertices at the same level;We give a complete characterization of the eigenvalues of the Laplacian matrix and adjacency matrix of G. They are the eigenvalues of leading principal submatrices of two nonnegative symmetric tridiagonal matrices of order k × k and the roots of some polynomials related with the characteristic polynomial of the referred submatrices. By application of the above mentioned results, we derive an upper bound on the largest eigenvalue of a graph defined by a weighted tree and a weighted triangle attached, by one of its vertices, to a pendant vertex of the tree. © 2008 Elsevier Inc. All rights reserved.
URI: http://hdl.handle.net/10773/4282
ISSN: 0024-3795
publisher version/DOI: http://www.sciencedirect.com/science/article/pii/S002437950800013X
source: Linear Algebra and Its Applications
appears in collectionsMAT - Artigos

files in this item

file description sizeformat
On the spectra of Some graphs like weighted rooted trees.pdfficheiro eletrónico213.22 kBAdobe PDFview/open
Restrict Access. You can Request a copy!
statistics

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

 

Valid XHTML 1.0! RCAAP OpenAIRE DeGóis
ria-repositorio@ua.pt - Copyright ©   Universidade de Aveiro - RIA Statistics - Powered by MIT's DSpace software, Version 1.6.2