Diameter-girth sufficient conditions for optimal extraconnectivity in graphs

For a connected graph G, the rth extraconnectivity r(G)is defined asthe minimum cardinality of a cutset X such that all remaining components after the deletion of the vertices of X have at least r + 1 vertices. The standard connectivity and superconnectivity correspond to 0(G) and 1(G), respectively...

Descripción completa

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:2008
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/163348
Acceso en línea:https://hdl.handle.net/11441/163348
https://doi.org/10.1016/j.disc.2007.07.012
Access Level:acceso abierto
Palabra clave:Connectivity
Superconnectivity
Cutset
Diameter
Girth
id ES_1026b9be116dfdcc1caf4fec77443a97
oai_identifier_str oai:idus.us.es:11441/163348
network_acronym_str ES
network_name_str España
repository_id_str
spelling Diameter-girth sufficient conditions for optimal extraconnectivity in graphsBalbuena, C.Cera López, MartínDiánez Martínez, Ana RosaGarcía Vázquez, PedroMarcote, X.ConnectivitySuperconnectivityCutsetDiameterGirthFor a connected graph G, the rth extraconnectivity r(G)is defined asthe minimum cardinality of a cutset X such that all remaining components after the deletion of the vertices of X have at least r + 1 vertices. The standard connectivity and superconnectivity correspond to 0(G) and 1(G), respectively. The minimum r-tree degree of G, denoted by r(G), is the minimum cardinality of N(T ) taken over all trees T ⊆ G of order |V (T )| = r + 1, N(T ) being the set of vertices not in T that are neighbors of some vertex of T. When r = 1, any such considered tree is just an edge of G. Then, 1(G) is equal to the so-called minimum edge-degree of G, defined as (G) = min{d(u) + d(v) − 2 : uv ∈ E(G)}, where d(u) stands for the degree of vertex u. A graph G is said to be optimally r-extraconnected, for short r-optimal, if r(G) r(G). In this paper, we present some sufficient conditions that guarantee r(G) r(G) for r 2. These results improve some previous related ones, and can be seen as a complement of some others which were obtained by the authors for r = 1.North Holland (Elsevier)Matemática Aplicada I2008info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/163348https://doi.org/10.1016/j.disc.2007.07.012reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésDiscrete Mathematics, 308 (16), 3526-3536.https://www.sciencedirect.com/science/article/pii/S0012365X07004979?via%3Dihubinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/1633482026-06-17T12:51:07Z
dc.title.none.fl_str_mv Diameter-girth sufficient conditions for optimal extraconnectivity in graphs
title Diameter-girth sufficient conditions for optimal extraconnectivity in graphs
spellingShingle Diameter-girth sufficient conditions for optimal extraconnectivity in graphs
Balbuena, C.
Connectivity
Superconnectivity
Cutset
Diameter
Girth
title_short Diameter-girth sufficient conditions for optimal extraconnectivity in graphs
title_full Diameter-girth sufficient conditions for optimal extraconnectivity in graphs
title_fullStr Diameter-girth sufficient conditions for optimal extraconnectivity in graphs
title_full_unstemmed Diameter-girth sufficient conditions for optimal extraconnectivity in graphs
title_sort Diameter-girth sufficient conditions for optimal extraconnectivity in graphs
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 Connectivity
Superconnectivity
Cutset
Diameter
Girth
topic Connectivity
Superconnectivity
Cutset
Diameter
Girth
description For a connected graph G, the rth extraconnectivity r(G)is defined asthe minimum cardinality of a cutset X such that all remaining components after the deletion of the vertices of X have at least r + 1 vertices. The standard connectivity and superconnectivity correspond to 0(G) and 1(G), respectively. The minimum r-tree degree of G, denoted by r(G), is the minimum cardinality of N(T ) taken over all trees T ⊆ G of order |V (T )| = r + 1, N(T ) being the set of vertices not in T that are neighbors of some vertex of T. When r = 1, any such considered tree is just an edge of G. Then, 1(G) is equal to the so-called minimum edge-degree of G, defined as (G) = min{d(u) + d(v) − 2 : uv ∈ E(G)}, where d(u) stands for the degree of vertex u. A graph G is said to be optimally r-extraconnected, for short r-optimal, if r(G) r(G). In this paper, we present some sufficient conditions that guarantee r(G) r(G) for r 2. These results improve some previous related ones, and can be seen as a complement of some others which were obtained by the authors for r = 1.
publishDate 2008
dc.date.none.fl_str_mv 2008
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/11441/163348
https://doi.org/10.1016/j.disc.2007.07.012
url https://hdl.handle.net/11441/163348
https://doi.org/10.1016/j.disc.2007.07.012
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Discrete Mathematics, 308 (16), 3526-3536.
https://www.sciencedirect.com/science/article/pii/S0012365X07004979?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
_version_ 1869403493733761024
score 15,812429

Similares en LA Referencia