dc.contributor.author Hamidoune, Yahya Ould dc.contributor.author Lladó Sánchez, Ana M. dc.contributor.author López Masip, Susana Clara dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV dc.date.accessioned 2011-07-15T17:35:11Z dc.date.available 2011-07-15T17:35:11Z dc.date.created 2011-06 dc.date.issued 2011-06 dc.identifier.citation Hamidoune, Y.O.; Llado, A.; López, S.C. Vertex-Transitive Graphs That Remain Connected After Failure of a Vertex and Its Neighbors. "Journal of graph theory", Juny 2011, vol. 67, núm. 2, p. 124-138. dc.identifier.issn 0364-9024 dc.identifier.uri http://hdl.handle.net/2117/12985 dc.description.abstract A d-regular graph is said to be superconnected if any disconnecting subset with cardinality at most d is formed by the neighbors of some vertex. A superconnected graph that remains connected after the failure of a vertex and its neighbors will be called vosperian. Let Γ be a vertex-transitive graph of degree d with order at least d+4. We give necessary and sufficient conditions for the vosperianity of Γ. Moreover, assuming that distinct vertices have distinct neighbors, we show that Γ is vosperian if and only if it is superconnected. Let G be a group and let S⊂G\{1} with S=S−1. We show that the Cayley graph, Cay(G, S), defined on G by S is vosperian if and only if G\(S∪{1}) is not a progression and for every non-trivial subgroup H and every a∈G, If moreover S is aperiodic, then Cay(G, S) is vosperian if and only if it is superconnected. dc.format.extent 15 p. dc.language.iso eng dc.publisher Wiley InterScience dc.rights Attribution-NonCommercial-NoDerivs 3.0 Spain dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes espectrals dc.subject.lcsh Graph algorithms dc.subject.lcsh Spectral theory (Mathematics) dc.title Vertex-Transitive Graphs That Remain Connected After Failure of a Vertex and Its Neighbors dc.type Article dc.subject.lemac Topologia algebraica dc.subject.lemac Teoria espectral (Matemàtica) dc.contributor.group Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions dc.identifier.doi 10.1002/jgt.20521 dc.description.peerreviewed Peer Reviewed dc.rights.access Restricted access - publisher's policy local.identifier.drac 5797085 dc.description.version Postprint (published version) local.citation.author Hamidoune, Y.O.; Llado, A.; López, S.C. local.citation.publicationName Journal of graph theory local.citation.volume 67 local.citation.number 2 local.citation.startingPage 124 local.citation.endingPage 138
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