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Vertex-transitive graphs that remain connected after failure of a vertex an its neighbors
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 | 2011-02-23T12:48:49Z |
dc.date.available | 2011-02-23T12:48:49Z |
dc.date.created | 2010 |
dc.date.issued | 2010 |
dc.identifier.citation | Hamidoune, Y.O.; Llado, A.; López, S.C. Vertex-transitive graphs that remain connected after failure of a vertex an its neighbors. "Journal of graph theory", 2010. |
dc.identifier.issn | 0364-9024 |
dc.identifier.uri | http://hdl.handle.net/2117/11507 |
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 $\Gamma$ be a vertex-transitive graph of degree d with order at least d+4. We give necessary and sufficient conditions for the vosperianity of $\Gamma$. Moreover, assuming that distinct vertices have distinct neighbors, we show that $\Gamma$ 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, |(H∪Ha)(S∪{1})|≥min(|G|−1, |H∪Ha|+|S|+1). If moreover S is aperiodic, then Cay(G,S) is vosperian if and only if it is superconnected. |
dc.language.iso | eng |
dc.publisher | Wiley InterScience |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
dc.subject.lcsh | Cayley graphs |
dc.subject.lcsh | Atom |
dc.subject.lcsh | Calculus of variations |
dc.title | Vertex-transitive graphs that remain connected after failure of a vertex an its neighbors |
dc.type | Article |
dc.subject.lemac | Grafs, Teoria de |
dc.subject.lemac | Àtoms |
dc.subject.lemac | Càlcul de variacions |
dc.contributor.group | Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
dc.identifier.doi | 10.1002/jgt.20521 |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 2592323 |
dc.description.version | Postprint (published version) |
local.citation.author | Hamidoune, Y.O.; Llado, A.; López, S.C. |
local.citation.publicationName | Journal of graph theory |
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