On the restricted connectivity and superconnectivity in graphs with given girth

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dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
dc.contributor	Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.contributor.author	Balbuena Martínez, Maria Camino Teófila
dc.contributor.author	Cera, M
dc.contributor.author	Diánez, A
dc.contributor.author	García-Vázquez, P
dc.contributor.author	Marcote Ordax, Francisco Javier
dc.date	2007-03
dc.identifier.citation	Balbuena, M. [et al.]. On the restricted connectivity and superconnectivity in graphs with given girth. "Discrete mathematics", Març 2007, vol. 307, núm. 6, p. 659-667.
dc.identifier.citation	0012-365X
dc.identifier.citation	10.1016/j.disc.2006.07.016
dc.identifier.uri	http://hdl.handle.net/2117/18915
dc.language.iso	eng
dc.relation	http://www.sciencedirect.com/science/article/pii/S0012365X06006017
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
dc.subject	Superconnectivity
dc.subject	Restricted connectivity
dc.subject	Connectivitat
dc.title	On the restricted connectivity and superconnectivity in graphs with given girth
dc.type	info:eu-repo/semantics/publishedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	"Discrete Mathemetics Top Cited Article 2005-2010"
dc.description.abstract	The restricted connectivity κ′(G)κ′(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 uu has all its neighbors in X; the superconnectivity κ1(G)κ1(G) is defined similarly, this time considering only vertices uu in G-XG-X, hence κ1(G)⩽κ′(G)κ1(G)⩽κ′(G). The minimum edge-degree of G is ξ(G)=min{d(u)+d(v)-2:uv∈E(G)}ξ(G)=min{d(u)+d(v)-2:uv∈E(G)}, d(u)d(u) standing for the degree of a vertex uu. In this paper, several sufficient conditions yielding κ1(G)⩾ξ(G)κ1(G)⩾ξ(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 κ1(G)=κ′(G)=ξ(G)κ1(G)=κ′(G)=ξ(G) under some additional constraints.
dc.description.abstract	Peer Reviewed
dc.description.abstract	Award-winning

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