Locating Eigenvalues of Perturbed Laplacian Matrices of Trees

Locating Eigenvalues of Perturbed Laplacian Matrices of Trees

ABSTRACT We give a linear time algorithm to compute the number of eigenvalues of any perturbed Laplacian matrix of a tree in a given real interval. The algorithm can be applied to weighted or unweighted trees. Using our method we characterize the trees that have up to 5 distinct eigenvalues with respect to a family of perturbed Laplacian matrices that includes the adjacency and normalized Laplacian matrices as special cases, among others.

Saved in:
Bibliographic Details
Main Authors: BRAGA,R.O., RODRIGUES,V.M.
Format: Digital revista
Language:English
Published: Sociedade Brasileira de Matemática Aplicada e Computacional 2017
Online Access:http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000300479
Tags: Add Tag
No Tags, Be the first to tag this record!
id oai:scielo:S2179-84512017000300479
record_format ojs
spelling oai:scielo:S2179-845120170003004792018-02-08Locating Eigenvalues of Perturbed Laplacian Matrices of TreesBRAGA,R.O.RODRIGUES,V.M. perturbed Laplacian matrix eigenvalue location trees ABSTRACT We give a linear time algorithm to compute the number of eigenvalues of any perturbed Laplacian matrix of a tree in a given real interval. The algorithm can be applied to weighted or unweighted trees. Using our method we characterize the trees that have up to 5 distinct eigenvalues with respect to a family of perturbed Laplacian matrices that includes the adjacency and normalized Laplacian matrices as special cases, among others.info:eu-repo/semantics/openAccessSociedade Brasileira de Matemática Aplicada e ComputacionalTEMA (São Carlos) v.18 n.3 20172017-12-01info:eu-repo/semantics/articletext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000300479en10.5540/tema.2017.018.03.0479
institution SCIELO
collection OJS
country Brasil
countrycode BR
component Revista
access En linea
databasecode rev-scielo-br
tag revista
region America del Sur
libraryname SciELO
language English
format Digital
author BRAGA,R.O.
RODRIGUES,V.M.
spellingShingle BRAGA,R.O.
RODRIGUES,V.M.
Locating Eigenvalues of Perturbed Laplacian Matrices of Trees
author_facet BRAGA,R.O.
RODRIGUES,V.M.
author_sort BRAGA,R.O.
title Locating Eigenvalues of Perturbed Laplacian Matrices of Trees
title_short Locating Eigenvalues of Perturbed Laplacian Matrices of Trees
title_full Locating Eigenvalues of Perturbed Laplacian Matrices of Trees
title_fullStr Locating Eigenvalues of Perturbed Laplacian Matrices of Trees
title_full_unstemmed Locating Eigenvalues of Perturbed Laplacian Matrices of Trees
title_sort locating eigenvalues of perturbed laplacian matrices of trees
description ABSTRACT We give a linear time algorithm to compute the number of eigenvalues of any perturbed Laplacian matrix of a tree in a given real interval. The algorithm can be applied to weighted or unweighted trees. Using our method we characterize the trees that have up to 5 distinct eigenvalues with respect to a family of perturbed Laplacian matrices that includes the adjacency and normalized Laplacian matrices as special cases, among others.
publisher Sociedade Brasileira de Matemática Aplicada e Computacional
publishDate 2017
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000300479
work_keys_str_mv AT bragaro locatingeigenvaluesofperturbedlaplacianmatricesoftrees
AT rodriguesvm locatingeigenvaluesofperturbedlaplacianmatricesoftrees
_version_ 1756439518868668416

Similar Items