Computing the Determinant of the Distance Matrix of a Bicyclic Graph

Autores
Dratman, Ezequiel; Grippo, Luciano Norberto; Safe, Martin Dario; da Silva Jr., Celso M; Del Vecchio, Renata R.
Año de publicación
2019
Idioma
inglés
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
Let G be a connected graph with vertex set V = {v1, ..., vn}. The distance d(vi, vj) between two vertices vi and vj is the number of edges of a shortest path linking them. The distance matrix of G is the n × n matrix such that its (i, j)-entry is equal to d(vi, vj). A formula to compute the determinant of this matrix in terms of the number of vertices was found when the graph either is a tree or is a unicyclic graph. For a byciclic graph, the determinant is known in the case where the cycles have no common edges. In this paper, we present some advances for the remaining cases; i.e., when the cycles share at least one edge. We also present a conjecture for the unsolved cases.
Fil: Dratman, Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Grippo, Luciano Norberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Safe, Martin Dario. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: da Silva Jr., Celso M. Centro Federal de Educação Tecnológica; Brasil
Fil: Del Vecchio, Renata R.. Universidade Federal Fluminense; Brasil
LAGOS 2019: X Latin and American Algorithms, Graphs and Optimization Symposium
Belo Horizonte
Brasil
Universidad Federal de Minas Gerais
Materia
bicyclic graphs
determinant
distance matrix
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/130172
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/130172
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Computing the Determinant of the Distance Matrix of a Bicyclic GraphDratman, EzequielGrippo, Luciano NorbertoSafe, Martin Darioda Silva Jr., Celso MDel Vecchio, Renata R.bicyclic graphsdeterminantdistance matrixhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let G be a connected graph with vertex set V = {v1, ..., vn}. The distance d(vi, vj) between two vertices vi and vj is the number of edges of a shortest path linking them. The distance matrix of G is the n × n matrix such that its (i, j)-entry is equal to d(vi, vj). A formula to compute the determinant of this matrix in terms of the number of vertices was found when the graph either is a tree or is a unicyclic graph. For a byciclic graph, the determinant is known in the case where the cycles have no common edges. In this paper, we present some advances for the remaining cases; i.e., when the cycles share at least one edge. We also present a conjecture for the unsolved cases.Fil: Dratman, Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Grippo, Luciano Norberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Safe, Martin Dario. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: da Silva Jr., Celso M. Centro Federal de Educação Tecnológica; BrasilFil: Del Vecchio, Renata R.. Universidade Federal Fluminense; BrasilLAGOS 2019: X Latin and American Algorithms, Graphs and Optimization SymposiumBelo HorizonteBrasilUniversidad Federal de Minas GeraisElsevierCoutinho, GabrielKohayakawa, Yoshiharudos Santos, Vinicius2019info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObjectSimposioJournalhttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/130172Computing the Determinant of the Distance Matrix of a Bicyclic Graph; LAGOS 2019: X Latin and American Algorithms, Graphs and Optimization Symposium; Belo Horizonte; Brasil; 20191571-0661CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://doi.org/10.1016/j.entcs.2019.08.037info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/journal/electronic-notes-in-theoretical-computer-science/vol/346/suppl/Cinfo:eu-repo/semantics/altIdentifier/url/http://www.lagos2019.dcc.ufmg.br/Internacionalinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:20:03Zoai:ri.conicet.gov.ar:11336/130172instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:20:03.849CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Computing the Determinant of the Distance Matrix of a Bicyclic Graph
title Computing the Determinant of the Distance Matrix of a Bicyclic Graph
spellingShingle Computing the Determinant of the Distance Matrix of a Bicyclic Graph
Dratman, Ezequiel
bicyclic graphs
determinant
distance matrix
title_short Computing the Determinant of the Distance Matrix of a Bicyclic Graph
title_full Computing the Determinant of the Distance Matrix of a Bicyclic Graph
title_fullStr Computing the Determinant of the Distance Matrix of a Bicyclic Graph
title_full_unstemmed Computing the Determinant of the Distance Matrix of a Bicyclic Graph
title_sort Computing the Determinant of the Distance Matrix of a Bicyclic Graph
dc.creator.none.fl_str_mv Dratman, Ezequiel
Grippo, Luciano Norberto
Safe, Martin Dario
da Silva Jr., Celso M
Del Vecchio, Renata R.
author Dratman, Ezequiel
author_facet Dratman, Ezequiel
Grippo, Luciano Norberto
Safe, Martin Dario
da Silva Jr., Celso M
Del Vecchio, Renata R.
author_role author
author2 Grippo, Luciano Norberto
Safe, Martin Dario
da Silva Jr., Celso M
Del Vecchio, Renata R.
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Coutinho, Gabriel
Kohayakawa, Yoshiharu
dos Santos, Vinicius
dc.subject.none.fl_str_mv bicyclic graphs
determinant
distance matrix
topic bicyclic graphs
determinant
distance matrix
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let G be a connected graph with vertex set V = {v1, ..., vn}. The distance d(vi, vj) between two vertices vi and vj is the number of edges of a shortest path linking them. The distance matrix of G is the n × n matrix such that its (i, j)-entry is equal to d(vi, vj). A formula to compute the determinant of this matrix in terms of the number of vertices was found when the graph either is a tree or is a unicyclic graph. For a byciclic graph, the determinant is known in the case where the cycles have no common edges. In this paper, we present some advances for the remaining cases; i.e., when the cycles share at least one edge. We also present a conjecture for the unsolved cases.
Fil: Dratman, Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Grippo, Luciano Norberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Safe, Martin Dario. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: da Silva Jr., Celso M. Centro Federal de Educação Tecnológica; Brasil
Fil: Del Vecchio, Renata R.. Universidade Federal Fluminense; Brasil
LAGOS 2019: X Latin and American Algorithms, Graphs and Optimization Symposium
Belo Horizonte
Brasil
Universidad Federal de Minas Gerais
description Let G be a connected graph with vertex set V = {v1, ..., vn}. The distance d(vi, vj) between two vertices vi and vj is the number of edges of a shortest path linking them. The distance matrix of G is the n × n matrix such that its (i, j)-entry is equal to d(vi, vj). A formula to compute the determinant of this matrix in terms of the number of vertices was found when the graph either is a tree or is a unicyclic graph. For a byciclic graph, the determinant is known in the case where the cycles have no common edges. In this paper, we present some advances for the remaining cases; i.e., when the cycles share at least one edge. We also present a conjecture for the unsolved cases.
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/conferenceObject
Simposio
Journal
http://purl.org/coar/resource_type/c_5794
info:ar-repo/semantics/documentoDeConferencia
status_str publishedVersion
format conferenceObject
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/130172
Computing the Determinant of the Distance Matrix of a Bicyclic Graph; LAGOS 2019: X Latin and American Algorithms, Graphs and Optimization Symposium; Belo Horizonte; Brasil; 2019
1571-0661
CONICET Digital
CONICET
url http://hdl.handle.net/11336/130172
identifier_str_mv Computing the Determinant of the Distance Matrix of a Bicyclic Graph; LAGOS 2019: X Latin and American Algorithms, Graphs and Optimization Symposium; Belo Horizonte; Brasil; 2019
1571-0661
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://doi.org/10.1016/j.entcs.2019.08.037
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/journal/electronic-notes-in-theoretical-computer-science/vol/346/suppl/C
info:eu-repo/semantics/altIdentifier/url/http://www.lagos2019.dcc.ufmg.br/
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.coverage.none.fl_str_mv Internacional
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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