Distance mean-regular graphs

We introduce the concept of distance mean-regular graph, which can be seen as a generalization of both vertex-transitive and distance-regular graphs. Let G be a graph with vertex set V , diameter D, adjacency matrix A, and adjacency algebra A. Then, G is distance mean-regular when, for a given u ¿ V...

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Detalles Bibliográficos
Autores: Fiol Mora, Miquel Àngel|||0000-0003-1337-4952, Diego, Victor
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/91052
Acceso en línea:https://hdl.handle.net/2117/91052
https://dx.doi.org/10.1007/s10623-016-0208-5
Access Level:acceso abierto
Palabra clave:Graph theory
Combinatorial analysis
Distance-regular graph
Vertex-transitive graph
Distance mean-regular graph
Intersection mean-matrix
Adjacency Algebra
Spectrum
Interlacing
Grafs, Teoria de
Combinacions (Matemàtica)
Classificació AMS::05 Combinatorics::05C Graph theory
Classificació AMS::05 Combinatorics::05E Algebraic combinatorics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
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network_acronym_str ES
network_name_str España
repository_id_str
spelling Distance mean-regular graphsFiol Mora, Miquel Àngel|||0000-0003-1337-4952Diego, VictorGraph theoryCombinatorial analysisDistance-regular graphVertex-transitive graphDistance mean-regular graphIntersection mean-matrixAdjacency AlgebraSpectrumInterlacingGrafs, Teoria deCombinacions (Matemàtica)Classificació AMS::05 Combinatorics::05C Graph theoryClassificació AMS::05 Combinatorics::05E Algebraic combinatoricsÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafsÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::CombinatòriaWe introduce the concept of distance mean-regular graph, which can be seen as a generalization of both vertex-transitive and distance-regular graphs. Let G be a graph with vertex set V , diameter D, adjacency matrix A, and adjacency algebra A. Then, G is distance mean-regular when, for a given u ¿ V , the averages of the intersection numbers p h ij (u, v) = |Gi(u) n Gj (v)| (number of vertices at distance i from u and distance j from v) computed over all vertices v at a given distance h ¿ {0, 1, . . . , D} from u, do not depend on u. In this work we study some properties and characterizations of these graphs. For instance, it is shown that a distance mean-regular graph is always distance degree-regular, and we give a condition for the converse to be also true. Some algebraic and spectral properties of distance mean-regular graphs are also investigated. We show that, for distance mean regular-graphs, the role of the distance matrices of distance-regular graphs is played for the so-called distance mean-regular matrices. These matrices are computed from a sequence of orthogonal polynomials evaluated at the adjacency matrix of G and, hence, they generate a subalgebra of A. Some other algebras associated to distance mean-regular graphs are also characterized.Peer Reviewed20162016-01-0120162016-10-25journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/91052https://dx.doi.org/10.1007/s10623-016-0208-5reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/910522026-05-27T15:37:01Z
dc.title.none.fl_str_mv Distance mean-regular graphs
title Distance mean-regular graphs
spellingShingle Distance mean-regular graphs
Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
Graph theory
Combinatorial analysis
Distance-regular graph
Vertex-transitive graph
Distance mean-regular graph
Intersection mean-matrix
Adjacency Algebra
Spectrum
Interlacing
Grafs, Teoria de
Combinacions (Matemàtica)
Classificació AMS::05 Combinatorics::05C Graph theory
Classificació AMS::05 Combinatorics::05E Algebraic combinatorics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
title_short Distance mean-regular graphs
title_full Distance mean-regular graphs
title_fullStr Distance mean-regular graphs
title_full_unstemmed Distance mean-regular graphs
title_sort Distance mean-regular graphs
dc.creator.none.fl_str_mv Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
Diego, Victor
author Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
author_facet Fiol Mora, Miquel Àngel|||0000-0003-1337-4952
Diego, Victor
author_role author
author2 Diego, Victor
author2_role author
dc.subject.none.fl_str_mv Graph theory
Combinatorial analysis
Distance-regular graph
Vertex-transitive graph
Distance mean-regular graph
Intersection mean-matrix
Adjacency Algebra
Spectrum
Interlacing
Grafs, Teoria de
Combinacions (Matemàtica)
Classificació AMS::05 Combinatorics::05C Graph theory
Classificació AMS::05 Combinatorics::05E Algebraic combinatorics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
topic Graph theory
Combinatorial analysis
Distance-regular graph
Vertex-transitive graph
Distance mean-regular graph
Intersection mean-matrix
Adjacency Algebra
Spectrum
Interlacing
Grafs, Teoria de
Combinacions (Matemàtica)
Classificació AMS::05 Combinatorics::05C Graph theory
Classificació AMS::05 Combinatorics::05E Algebraic combinatorics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
description We introduce the concept of distance mean-regular graph, which can be seen as a generalization of both vertex-transitive and distance-regular graphs. Let G be a graph with vertex set V , diameter D, adjacency matrix A, and adjacency algebra A. Then, G is distance mean-regular when, for a given u ¿ V , the averages of the intersection numbers p h ij (u, v) = |Gi(u) n Gj (v)| (number of vertices at distance i from u and distance j from v) computed over all vertices v at a given distance h ¿ {0, 1, . . . , D} from u, do not depend on u. In this work we study some properties and characterizations of these graphs. For instance, it is shown that a distance mean-regular graph is always distance degree-regular, and we give a condition for the converse to be also true. Some algebraic and spectral properties of distance mean-regular graphs are also investigated. We show that, for distance mean regular-graphs, the role of the distance matrices of distance-regular graphs is played for the so-called distance mean-regular matrices. These matrices are computed from a sequence of orthogonal polynomials evaluated at the adjacency matrix of G and, hence, they generate a subalgebra of A. Some other algebras associated to distance mean-regular graphs are also characterized.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-01-01
2016
2016-10-25
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/91052
https://dx.doi.org/10.1007/s10623-016-0208-5
url https://hdl.handle.net/2117/91052
https://dx.doi.org/10.1007/s10623-016-0208-5
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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