On Vosperian and Superconnected Vertex-Transitive Digraphs

We investigate the structure of a digraph having a transitive automorphism group where every cutset of minimal cardinality consists of all successors or all predecessors of some vertex. We give a complete characterization of vosperian arc-transitive digraphs. It states that an arc-transitive strongl...

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Detalles Bibliográficos
Autores: Hamidoune, Yahya Ould, Lladó, Anna, López Masip, Susana-Clara
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2013
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10459.1/66453
Acceso en línea:https://doi.org/10.1007/s00373-011-1104-4
http://hdl.handle.net/10459.1/66453
Access Level:acceso abierto
Palabra clave:Arc-transitive
Cayley digraph
Isoperimetric connectivity
Superconnected
Vosperian
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spelling On Vosperian and Superconnected Vertex-Transitive DigraphsHamidoune, Yahya OuldLladó, AnnaLópez Masip, Susana-ClaraArc-transitiveCayley digraphIsoperimetric connectivitySuperconnectedVosperianWe investigate the structure of a digraph having a transitive automorphism group where every cutset of minimal cardinality consists of all successors or all predecessors of some vertex. We give a complete characterization of vosperian arc-transitive digraphs. It states that an arc-transitive strongly connected digraph is vosperian if and only if it is irreducible. In particular, this is the case if the degree is coprime with the order of the digraph. We give also a complete characterization of vosperian Cayley digraphs and a complete characterization of irreducible superconnected Cayley digraphs. These two last characterizations extend the corresponding ones in Abelian Cayley digraphs and the ones in the undirected case.Research supported by the Ministry of Science and Innovation, Spain under project MTM2008-06620-C03-01/MTM and the Catalan Research Council under project 2009SGR01387. Research done when the last author was visiting Université Pierre et Marie Curie, E. Combinatoire, Paris, supported by the Ministry of Science and Innovation, Spain under the National Mobility Programme of Human Resources, Spanish National Programme I-D-I 2008–2011.Springer2019201920132019info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://doi.org/10.1007/s00373-011-1104-4http://hdl.handle.net/10459.1/66453http://hdl.handle.net/10459.1/66453reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)Inglésinfo:eu-repo/grantAgreement/MICINN//MTM2008-06620-C03-01Versió postprint del document publicat https://doi.org/10.1007/s00373-011-1104-4Graphs and Combinatorics, 2013, vol. 29, num. 2, p. 241-251(c) Springer, 2013info:eu-repo/semantics/openAccessoai:recercat.cat:10459.1/664532026-05-29T05:05:01Z
dc.title.none.fl_str_mv On Vosperian and Superconnected Vertex-Transitive Digraphs
title On Vosperian and Superconnected Vertex-Transitive Digraphs
spellingShingle On Vosperian and Superconnected Vertex-Transitive Digraphs
Hamidoune, Yahya Ould
Arc-transitive
Cayley digraph
Isoperimetric connectivity
Superconnected
Vosperian
title_short On Vosperian and Superconnected Vertex-Transitive Digraphs
title_full On Vosperian and Superconnected Vertex-Transitive Digraphs
title_fullStr On Vosperian and Superconnected Vertex-Transitive Digraphs
title_full_unstemmed On Vosperian and Superconnected Vertex-Transitive Digraphs
title_sort On Vosperian and Superconnected Vertex-Transitive Digraphs
dc.creator.none.fl_str_mv Hamidoune, Yahya Ould
Lladó, Anna
López Masip, Susana-Clara
author Hamidoune, Yahya Ould
author_facet Hamidoune, Yahya Ould
Lladó, Anna
López Masip, Susana-Clara
author_role author
author2 Lladó, Anna
López Masip, Susana-Clara
author2_role author
author
dc.subject.none.fl_str_mv Arc-transitive
Cayley digraph
Isoperimetric connectivity
Superconnected
Vosperian
topic Arc-transitive
Cayley digraph
Isoperimetric connectivity
Superconnected
Vosperian
description We investigate the structure of a digraph having a transitive automorphism group where every cutset of minimal cardinality consists of all successors or all predecessors of some vertex. We give a complete characterization of vosperian arc-transitive digraphs. It states that an arc-transitive strongly connected digraph is vosperian if and only if it is irreducible. In particular, this is the case if the degree is coprime with the order of the digraph. We give also a complete characterization of vosperian Cayley digraphs and a complete characterization of irreducible superconnected Cayley digraphs. These two last characterizations extend the corresponding ones in Abelian Cayley digraphs and the ones in the undirected case.
publishDate 2013
dc.date.none.fl_str_mv 2013
2019
2019
2019
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://doi.org/10.1007/s00373-011-1104-4
http://hdl.handle.net/10459.1/66453
http://hdl.handle.net/10459.1/66453
url https://doi.org/10.1007/s00373-011-1104-4
http://hdl.handle.net/10459.1/66453
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MICINN//MTM2008-06620-C03-01
Versió postprint del document publicat https://doi.org/10.1007/s00373-011-1104-4
Graphs and Combinatorics, 2013, vol. 29, num. 2, p. 241-251
dc.rights.none.fl_str_mv (c) Springer, 2013
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Springer, 2013
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
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repository.mail.fl_str_mv
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