On average connectivity of the strong product of graphs

The average connectivity κ(G) of a graph G is the average, over all pairs of vertices, of the maximum number of internally disjoint paths connecting these vertices. The connectivity κ(G) can be seen as the minimum, over all pairs of vertices, of the maximum number of internally disjoint paths connec...

ver descrição completa

Detalhes bibliográficos
Autores: Abajo Casado, María Encarnación, Moreno Casablanca, Rocío, Diánez Martínez, Ana Rosa, García Vázquez, Pedro
Formato: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2013
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/69459
Acesso em linha:https://hdl.handle.net/11441/69459
https://doi.org/10.1016/j.dam.2013.06.005
Access Level:acceso abierto
Palavra-chave:Average connectivity
Strong Product Graphs
Maximally connected graphs
Average degree
id ES_2db2434c6f4556095e712cd4b83ddf07
oai_identifier_str oai:idus.us.es:11441/69459
network_acronym_str ES
network_name_str España
repository_id_str
spelling On average connectivity of the strong product of graphsAbajo Casado, María EncarnaciónMoreno Casablanca, RocíoDiánez Martínez, Ana RosaGarcía Vázquez, PedroAverage connectivityStrong Product GraphsMaximally connected graphsAverage degreeThe average connectivity κ(G) of a graph G is the average, over all pairs of vertices, of the maximum number of internally disjoint paths connecting these vertices. The connectivity κ(G) can be seen as the minimum, over all pairs of vertices, of the maximum number of internally disjoint paths connecting these vertices. The connectivity and the average connectivity are upper bounded by the minimum degree δ(G) and the average degree d(G) of G, respectively. In this paper the average connectivity of the strong product G1 G2 of two connected graphs G1 and G2 is studied. A sharp lower bound for this parameter is obtained. As a consequence, we prove that κ(G1 G2) = d(G1 G2) if κ(Gi) = d(Gi), i = 1, 2. Also we deduce that κ(G1 G2) = δ(G1 G2) if κ(Gi) = δ(Gi), i = 1, 2.Ministerio de Educación y Ciencia MTM2011-28800-C02-02Generalitat de Cataluña 1298 SGR2009ElsevierMatemática Aplicada IFQM240: Invariantes en Teoria de Grafos y OptimizacionMinisterio de Educación y Ciencia (MEC). EspañaGeneralitat de Catalunya2013info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/69459https://doi.org/10.1016/j.dam.2013.06.005reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésDiscrete Applied Mathematics, 161 (18), 2795-2801.MTM2011-28800-C02-021298 SGR2009https://www.sciencedirect.com/science/article/pii/S0166218X13002837info:eu-repo/semantics/openAccessoai:idus.us.es:11441/694592026-06-17T12:51:07Z
dc.title.none.fl_str_mv On average connectivity of the strong product of graphs
title On average connectivity of the strong product of graphs
spellingShingle On average connectivity of the strong product of graphs
Abajo Casado, María Encarnación
Average connectivity
Strong Product Graphs
Maximally connected graphs
Average degree
title_short On average connectivity of the strong product of graphs
title_full On average connectivity of the strong product of graphs
title_fullStr On average connectivity of the strong product of graphs
title_full_unstemmed On average connectivity of the strong product of graphs
title_sort On average connectivity of the strong product of graphs
dc.creator.none.fl_str_mv Abajo Casado, María Encarnación
Moreno Casablanca, Rocío
Diánez Martínez, Ana Rosa
García Vázquez, Pedro
author Abajo Casado, María Encarnación
author_facet Abajo Casado, María Encarnación
Moreno Casablanca, Rocío
Diánez Martínez, Ana Rosa
García Vázquez, Pedro
author_role author
author2 Moreno Casablanca, Rocío
Diánez Martínez, Ana Rosa
García Vázquez, Pedro
author2_role author
author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
FQM240: Invariantes en Teoria de Grafos y Optimizacion
Ministerio de Educación y Ciencia (MEC). España
Generalitat de Catalunya
dc.subject.none.fl_str_mv Average connectivity
Strong Product Graphs
Maximally connected graphs
Average degree
topic Average connectivity
Strong Product Graphs
Maximally connected graphs
Average degree
description The average connectivity κ(G) of a graph G is the average, over all pairs of vertices, of the maximum number of internally disjoint paths connecting these vertices. The connectivity κ(G) can be seen as the minimum, over all pairs of vertices, of the maximum number of internally disjoint paths connecting these vertices. The connectivity and the average connectivity are upper bounded by the minimum degree δ(G) and the average degree d(G) of G, respectively. In this paper the average connectivity of the strong product G1 G2 of two connected graphs G1 and G2 is studied. A sharp lower bound for this parameter is obtained. As a consequence, we prove that κ(G1 G2) = d(G1 G2) if κ(Gi) = d(Gi), i = 1, 2. Also we deduce that κ(G1 G2) = δ(G1 G2) if κ(Gi) = δ(Gi), i = 1, 2.
publishDate 2013
dc.date.none.fl_str_mv 2013
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/69459
https://doi.org/10.1016/j.dam.2013.06.005
url https://hdl.handle.net/11441/69459
https://doi.org/10.1016/j.dam.2013.06.005
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Discrete Applied Mathematics, 161 (18), 2795-2801.
MTM2011-28800-C02-02
1298 SGR2009
https://www.sciencedirect.com/science/article/pii/S0166218X13002837
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869405342712987648
score 15,198674

Registos relacionados