Change in vertex status after removal of another vertex in the general setting

Detalhes bibliográficos
Autor(a) principal: Johnson, Charles R.
Data de Publicação: 2021
Outros Autores: Saiago, Carlos M., Toyonaga, Kenji
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/135559
Resumo: In the theory of multiplicities for eigenvalues of symmetric matrices whose graph is a tree, it proved very useful to understand the change in status (Parter, neutral, or downer) of one vertex upon removal of another vertex of given status (both in case the two vertices are adjacent or non-adjacent). As the subject has evolved toward the study of more general matrices, over more general fields, with more general graphs, it is appropriate to resolve the same type of question in the more general settings. “Multiplicity” now means geometric multiplicity. Here, we give a complete resolution in three more general settings and compare these with the classical case (216 “Yes” or “No” results). As a consequence, several unexpected insights are recorded.
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spelling Change in vertex status after removal of another vertex in the general settingCombinatorially symmetricEigenvalueGeometric multiplicityGraph of a matrixTreeAlgebra and Number TheoryNumerical AnalysisGeometry and TopologyDiscrete Mathematics and CombinatoricsIn the theory of multiplicities for eigenvalues of symmetric matrices whose graph is a tree, it proved very useful to understand the change in status (Parter, neutral, or downer) of one vertex upon removal of another vertex of given status (both in case the two vertices are adjacent or non-adjacent). As the subject has evolved toward the study of more general matrices, over more general fields, with more general graphs, it is appropriate to resolve the same type of question in the more general settings. “Multiplicity” now means geometric multiplicity. Here, we give a complete resolution in three more general settings and compare these with the classical case (216 “Yes” or “No” results). As a consequence, several unexpected insights are recorded.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNJohnson, Charles R.Saiago, Carlos M.Toyonaga, Kenji2022-12-17T01:31:38Z2021-03-012021-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article18application/pdfhttp://hdl.handle.net/10362/135559eng0024-3795PURE: 27629983https://doi.org/10.1016/j.laa.2020.11.023info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-03-11T05:13:56Zoai:run.unl.pt:10362/135559Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:48:27.263671Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Change in vertex status after removal of another vertex in the general setting
title Change in vertex status after removal of another vertex in the general setting
spellingShingle Change in vertex status after removal of another vertex in the general setting
Johnson, Charles R.
Combinatorially symmetric
Eigenvalue
Geometric multiplicity
Graph of a matrix
Tree
Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics
title_short Change in vertex status after removal of another vertex in the general setting
title_full Change in vertex status after removal of another vertex in the general setting
title_fullStr Change in vertex status after removal of another vertex in the general setting
title_full_unstemmed Change in vertex status after removal of another vertex in the general setting
title_sort Change in vertex status after removal of another vertex in the general setting
author Johnson, Charles R.
author_facet Johnson, Charles R.
Saiago, Carlos M.
Toyonaga, Kenji
author_role author
author2 Saiago, Carlos M.
Toyonaga, Kenji
author2_role author
author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
DM - Departamento de Matemática
RUN
dc.contributor.author.fl_str_mv Johnson, Charles R.
Saiago, Carlos M.
Toyonaga, Kenji
dc.subject.por.fl_str_mv Combinatorially symmetric
Eigenvalue
Geometric multiplicity
Graph of a matrix
Tree
Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics
topic Combinatorially symmetric
Eigenvalue
Geometric multiplicity
Graph of a matrix
Tree
Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics
description In the theory of multiplicities for eigenvalues of symmetric matrices whose graph is a tree, it proved very useful to understand the change in status (Parter, neutral, or downer) of one vertex upon removal of another vertex of given status (both in case the two vertices are adjacent or non-adjacent). As the subject has evolved toward the study of more general matrices, over more general fields, with more general graphs, it is appropriate to resolve the same type of question in the more general settings. “Multiplicity” now means geometric multiplicity. Here, we give a complete resolution in three more general settings and compare these with the classical case (216 “Yes” or “No” results). As a consequence, several unexpected insights are recorded.
publishDate 2021
dc.date.none.fl_str_mv 2021-03-01
2021-03-01T00:00:00Z
2022-12-17T01:31:38Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/135559
url http://hdl.handle.net/10362/135559
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0024-3795
PURE: 27629983
https://doi.org/10.1016/j.laa.2020.11.023
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