On the restricted connectivity and superconnectivity in graphs with given girth

The restricted connectivity (G) of a connected graph G is defined as the minimum cardinality of a vertex-cut over all vertex-cuts X such that no vertex u has all its neighbors in X; the superconnectivity 1(G) is defined similarly, this time considering only vertices u in G − X, hence 1(G) (G). The m...

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Detalles Bibliográficos
Autores: Balbuena, C., Cera López, Martín, Diánez Martínez, Ana Rosa, García Vázquez, Pedro, Marcote, X.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2007
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/163746
Acceso en línea:https://hdl.handle.net/11441/163746
https://doi.org/10.1016/j.disc.2006.07.016
Access Level:acceso abierto
Palabra clave:Superconnectivity
Restricted connectivity
Diameter
Girth
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spelling On the restricted connectivity and superconnectivity in graphs with given girthBalbuena, C.Cera López, MartínDiánez Martínez, Ana RosaGarcía Vázquez, PedroMarcote, X.SuperconnectivityRestricted connectivityDiameterGirthThe restricted connectivity (G) of a connected graph G is defined as the minimum cardinality of a vertex-cut over all vertex-cuts X such that no vertex u has all its neighbors in X; the superconnectivity 1(G) is defined similarly, this time considering only vertices u in G − X, hence 1(G) (G). The minimum edge-degree of G is (G) = min{d(u) + d(v) − 2 : uv ∈ E(G)}, d(u) standing for the degree of a vertex u. In this paper, several sufficient conditions yielding 1(G) (G) are given, improving a previous related result by Fiol et al. [Short paths and connectivity in graphs and digraphs, Ars Combin. 29B (1990) 17–31] and guaranteeing 1(G) = (G) = (G) under some additional constraints.North Holland (Elsevier)Matemática Aplicada I2007info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/163746https://doi.org/10.1016/j.disc.2006.07.016reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésDiscrete Mathematics, 307 (6), 659-667.https://www.sciencedirect.com/science/article/pii/S0012365X06006017?via%3Dihubinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/1637462026-06-17T12:51:07Z
dc.title.none.fl_str_mv On the restricted connectivity and superconnectivity in graphs with given girth
title On the restricted connectivity and superconnectivity in graphs with given girth
spellingShingle On the restricted connectivity and superconnectivity in graphs with given girth
Balbuena, C.
Superconnectivity
Restricted connectivity
Diameter
Girth
title_short On the restricted connectivity and superconnectivity in graphs with given girth
title_full On the restricted connectivity and superconnectivity in graphs with given girth
title_fullStr On the restricted connectivity and superconnectivity in graphs with given girth
title_full_unstemmed On the restricted connectivity and superconnectivity in graphs with given girth
title_sort On the restricted connectivity and superconnectivity in graphs with given girth
dc.creator.none.fl_str_mv Balbuena, C.
Cera López, Martín
Diánez Martínez, Ana Rosa
García Vázquez, Pedro
Marcote, X.
author Balbuena, C.
author_facet Balbuena, C.
Cera López, Martín
Diánez Martínez, Ana Rosa
García Vázquez, Pedro
Marcote, X.
author_role author
author2 Cera López, Martín
Diánez Martínez, Ana Rosa
García Vázquez, Pedro
Marcote, X.
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
dc.subject.none.fl_str_mv Superconnectivity
Restricted connectivity
Diameter
Girth
topic Superconnectivity
Restricted connectivity
Diameter
Girth
description The restricted connectivity (G) of a connected graph G is defined as the minimum cardinality of a vertex-cut over all vertex-cuts X such that no vertex u has all its neighbors in X; the superconnectivity 1(G) is defined similarly, this time considering only vertices u in G − X, hence 1(G) (G). The minimum edge-degree of G is (G) = min{d(u) + d(v) − 2 : uv ∈ E(G)}, d(u) standing for the degree of a vertex u. In this paper, several sufficient conditions yielding 1(G) (G) are given, improving a previous related result by Fiol et al. [Short paths and connectivity in graphs and digraphs, Ars Combin. 29B (1990) 17–31] and guaranteeing 1(G) = (G) = (G) under some additional constraints.
publishDate 2007
dc.date.none.fl_str_mv 2007
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/163746
https://doi.org/10.1016/j.disc.2006.07.016
url https://hdl.handle.net/11441/163746
https://doi.org/10.1016/j.disc.2006.07.016
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Discrete Mathematics, 307 (6), 659-667.
https://www.sciencedirect.com/science/article/pii/S0012365X06006017?via%3Dihub
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 North Holland (Elsevier)
publisher.none.fl_str_mv North Holland (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
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