Edge distance-regular graphs

Edge-distance-regularity is a concept recently introduced by the authors which is similar to that of distance-regularity, but now the graph is seen from each of its edges instead of from its vertices. More precisely, a graph Γ with adjacency matrix A is edge-distance-regular when it is distance-regu...

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Autores: Cámara Vallejo, Marc, Dalfó, Cristina, Fàbrega Canudas, José, Fiol Mora, Miguel Ángel, Garriga, Ernest
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2011
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:10459.1/72557
Acceso en línea:https://doi.org/10.1016/j.endm.2011.09.037
http://hdl.handle.net/10459.1/72557
Access Level:acceso abierto
Palabra clave:Distance-regularity
Local spectra
Predistance polynomials
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spelling Edge distance-regular graphsCámara Vallejo, MarcDalfó, CristinaFàbrega Canudas, JoséFiol Mora, Miguel ÁngelGarriga, ErnestDistance-regularityLocal spectraPredistance polynomialsEdge-distance-regularity is a concept recently introduced by the authors which is similar to that of distance-regularity, but now the graph is seen from each of its edges instead of from its vertices. More precisely, a graph Γ with adjacency matrix A is edge-distance-regular when it is distance-regular around each of its edges and with the same intersection numbers for any edge taken as a root. In this paper we study this concept, give some of its properties, such as the regularity of Γ, and derive some characterizations. In particular, it is shown that a graph is edge-distance-regular if and only if its k-incidence matrix is a polynomial of degree k in A multiplied by the (standard) incidence matrix. Also, the analogue of the spectral excess theorem for distance-regular graphs is proved, so giving a quasi-spectral characterization of edge-distance-regularity. Finally, it is shown that every nonbipartite graph which is both distance-regular and edge-distance-regular is a generalized odd graph.Supported by the Ministry of Science and Innovation of Spain under project MTM2008- 06620-C03-01 and by the Catalan Research Council under project 2009SGR01387Elsevier202120212011info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionhttps://doi.org/10.1016/j.endm.2011.09.037http://hdl.handle.net/10459.1/72557http://hdl.handle.net/10459.1/72557reponame: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/10.1016/j.endm.2011.09.037Electronic notes in discrete mathematics, 2011, vol. 38, p. 221-226.cc-by-nc-nd (c) Elsevier, 2011info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/oai:recercat.cat:10459.1/725572026-05-29T05:05:01Z
dc.title.none.fl_str_mv Edge distance-regular graphs
title Edge distance-regular graphs
spellingShingle Edge distance-regular graphs
Cámara Vallejo, Marc
Distance-regularity
Local spectra
Predistance polynomials
title_short Edge distance-regular graphs
title_full Edge distance-regular graphs
title_fullStr Edge distance-regular graphs
title_full_unstemmed Edge distance-regular graphs
title_sort Edge distance-regular graphs
dc.creator.none.fl_str_mv Cámara Vallejo, Marc
Dalfó, Cristina
Fàbrega Canudas, José
Fiol Mora, Miguel Ángel
Garriga, Ernest
author Cámara Vallejo, Marc
author_facet Cámara Vallejo, Marc
Dalfó, Cristina
Fàbrega Canudas, José
Fiol Mora, Miguel Ángel
Garriga, Ernest
author_role author
author2 Dalfó, Cristina
Fàbrega Canudas, José
Fiol Mora, Miguel Ángel
Garriga, Ernest
author2_role author
author
author
author
dc.subject.none.fl_str_mv Distance-regularity
Local spectra
Predistance polynomials
topic Distance-regularity
Local spectra
Predistance polynomials
description Edge-distance-regularity is a concept recently introduced by the authors which is similar to that of distance-regularity, but now the graph is seen from each of its edges instead of from its vertices. More precisely, a graph Γ with adjacency matrix A is edge-distance-regular when it is distance-regular around each of its edges and with the same intersection numbers for any edge taken as a root. In this paper we study this concept, give some of its properties, such as the regularity of Γ, and derive some characterizations. In particular, it is shown that a graph is edge-distance-regular if and only if its k-incidence matrix is a polynomial of degree k in A multiplied by the (standard) incidence matrix. Also, the analogue of the spectral excess theorem for distance-regular graphs is proved, so giving a quasi-spectral characterization of edge-distance-regularity. Finally, it is shown that every nonbipartite graph which is both distance-regular and edge-distance-regular is a generalized odd graph.
publishDate 2011
dc.date.none.fl_str_mv 2011
2021
2021
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/10.1016/j.endm.2011.09.037
http://hdl.handle.net/10459.1/72557
http://hdl.handle.net/10459.1/72557
url https://doi.org/10.1016/j.endm.2011.09.037
http://hdl.handle.net/10459.1/72557
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/10.1016/j.endm.2011.09.037
Electronic notes in discrete mathematics, 2011, vol. 38, p. 221-226.
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Elsevier, 2011
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/
rights_invalid_str_mv cc-by-nc-nd (c) Elsevier, 2011
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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
repository.name.fl_str_mv
repository.mail.fl_str_mv
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