The maximum number of Parter vertices of acyclic matrices

Detalhes bibliográficos
Autor(a) principal: Fonseca, Amélia
Data de Publicação: 2021
Outros Autores: Mestre, Ângela, Mohammadian, Ali, Perdigão, Cecília, Torres, Maria Manuel
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/132651
Resumo: The authors would like to thank anonymous referees for their helpful comments and suggestions which considerably improved the presentation of the paper. The authors except the third one were supported by Portuguese Funds through the Portuguese Foundation for Science and Technology (FCT). The first, second, and fifth authors were supported by FCT (Fundacao para a Ciencia e Tecnologia), under the project UIDB/04721/2020 (CEAFEL - Centro de Analise Funcional e Estruturas Lineares). The fourth author was supported within the scope of the project UIDB/00297/2020 (CMA - Centro de Matematica e Aplicacoes). This work was started in August 2017 while the third author was visiting CEAFEL at the Faculty of Sciences in the University of Lisbon. He is sincerely grateful to CEAFEL for the hospitality and support in August 2017 and March 2018. He also wishes to express his gratitude for the travel grant he received from the Institute for Research in Fundamental Sciences (IPM) in August 2017.
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spelling The maximum number of Parter vertices of acyclic matricesAcyclic matrixNullityParter vertexTreeTheoretical Computer ScienceDiscrete Mathematics and CombinatoricsThe authors would like to thank anonymous referees for their helpful comments and suggestions which considerably improved the presentation of the paper. The authors except the third one were supported by Portuguese Funds through the Portuguese Foundation for Science and Technology (FCT). The first, second, and fifth authors were supported by FCT (Fundacao para a Ciencia e Tecnologia), under the project UIDB/04721/2020 (CEAFEL - Centro de Analise Funcional e Estruturas Lineares). The fourth author was supported within the scope of the project UIDB/00297/2020 (CMA - Centro de Matematica e Aplicacoes). This work was started in August 2017 while the third author was visiting CEAFEL at the Faculty of Sciences in the University of Lisbon. He is sincerely grateful to CEAFEL for the hospitality and support in August 2017 and March 2018. He also wishes to express his gratitude for the travel grant he received from the Institute for Research in Fundamental Sciences (IPM) in August 2017.A vertex v of the underlying graph of a symmetric matrix A is called ‘Parter’ if the nullity of the matrix obtained from A by removing the row and column indexed by v is more than the nullity of A. Let A be a singular symmetric matrix with rank r whose underlying graph is a tree. It is known that the number of Parter vertices of A is at most r−1. We prove that when r is odd this number is at most r−2. We characterize the trees where these bounds are achieved.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNFonseca, AméliaMestre, ÂngelaMohammadian, AliPerdigão, CecíliaTorres, Maria Manuel2022-11-18T01:31:48Z2021-022021-02-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10362/132651eng0012-365XPURE: 26684081https://doi.org/10.1016/j.disc.2020.112198info: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:RCAAP2024-03-11T05:11:19Zoai:run.unl.pt:10362/132651Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:47:32.956339Repositório 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 The maximum number of Parter vertices of acyclic matrices
title The maximum number of Parter vertices of acyclic matrices
spellingShingle The maximum number of Parter vertices of acyclic matrices
Fonseca, Amélia
Acyclic matrix
Nullity
Parter vertex
Tree
Theoretical Computer Science
Discrete Mathematics and Combinatorics
title_short The maximum number of Parter vertices of acyclic matrices
title_full The maximum number of Parter vertices of acyclic matrices
title_fullStr The maximum number of Parter vertices of acyclic matrices
title_full_unstemmed The maximum number of Parter vertices of acyclic matrices
title_sort The maximum number of Parter vertices of acyclic matrices
author Fonseca, Amélia
author_facet Fonseca, Amélia
Mestre, Ângela
Mohammadian, Ali
Perdigão, Cecília
Torres, Maria Manuel
author_role author
author2 Mestre, Ângela
Mohammadian, Ali
Perdigão, Cecília
Torres, Maria Manuel
author2_role author
author
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 Fonseca, Amélia
Mestre, Ângela
Mohammadian, Ali
Perdigão, Cecília
Torres, Maria Manuel
dc.subject.por.fl_str_mv Acyclic matrix
Nullity
Parter vertex
Tree
Theoretical Computer Science
Discrete Mathematics and Combinatorics
topic Acyclic matrix
Nullity
Parter vertex
Tree
Theoretical Computer Science
Discrete Mathematics and Combinatorics
description The authors would like to thank anonymous referees for their helpful comments and suggestions which considerably improved the presentation of the paper. The authors except the third one were supported by Portuguese Funds through the Portuguese Foundation for Science and Technology (FCT). The first, second, and fifth authors were supported by FCT (Fundacao para a Ciencia e Tecnologia), under the project UIDB/04721/2020 (CEAFEL - Centro de Analise Funcional e Estruturas Lineares). The fourth author was supported within the scope of the project UIDB/00297/2020 (CMA - Centro de Matematica e Aplicacoes). This work was started in August 2017 while the third author was visiting CEAFEL at the Faculty of Sciences in the University of Lisbon. He is sincerely grateful to CEAFEL for the hospitality and support in August 2017 and March 2018. He also wishes to express his gratitude for the travel grant he received from the Institute for Research in Fundamental Sciences (IPM) in August 2017.
publishDate 2021
dc.date.none.fl_str_mv 2021-02
2021-02-01T00:00:00Z
2022-11-18T01:31:48Z
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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dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/132651
url http://hdl.handle.net/10362/132651
dc.language.iso.fl_str_mv eng
language eng
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PURE: 26684081
https://doi.org/10.1016/j.disc.2020.112198
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