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On almost distance-regular graphs
dc.contributor.author | Dalfó Simó, Cristina |
dc.contributor.author | Van Dam, Edwin |
dc.contributor.author | Fiol Mora, Miquel Àngel |
dc.contributor.author | Garriga Valle, Ernest |
dc.contributor.author | Gorissen, Bram |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
dc.date.accessioned | 2011-01-19T17:24:21Z |
dc.date.available | 2011-01-19T17:24:21Z |
dc.date.created | 2010 |
dc.date.issued | 2010 |
dc.identifier.citation | Dalfo, C. [et al.]. On almost distance-regular graphs. "Journal of combinatorial theory. Series A", 2010. |
dc.identifier.issn | 0097-3165 |
dc.identifier.uri | http://hdl.handle.net/2117/11111 |
dc.description.abstract | Distance-regular graphs are a key concept in Algebraic Combinatorics and have given rise to several generalizations, such as association schemes. Motivated by spectral and other algebraic characterizations of distance-regular graphs, we study ‘almost distanceregular graphs’. We use this name informally for graphs that share some regularity properties that are related to distance in the graph. For example, a known characterization of a distance-regular graph is the invariance of the number of walks of given length between vertices at a given distance, while a graph is called walk-regular if the number of closed walks of given length rooted at any given vertex is a constant. One of the concepts studied here is a generalization of both distance-regularity and walk-regularity called m-walkregularity. Another studied concept is that of m-partial distanceregularity or, informally, distance-regularity up to distance m. Using eigenvalues of graphs and the predistance polynomials, we discuss and relate these and other concepts of almost distance-regularity, such as their common generalization of ( ,m)-walk-regularity. We introduce the concepts of punctual distance-regularity and punctual walk-regularity as a fundament upon which almost distanceregular graphs are built. We provide examples that are mostly taken from the Foster census, a collection of symmetric cubic graphs. Two problems are posed that are related to the question of when almost distance-regular becomes whole distance-regular. We also give several characterizations of punctually distance-regular graphs that are generalizations of the spectral excess theorem. |
dc.language.iso | eng |
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::Matemàtica discreta::Teoria de grafs |
dc.subject.lcsh | Graph theory |
dc.subject.other | Distance-regular graph |
dc.subject.other | Walk-regular graph |
dc.subject.other | Eigenvalues |
dc.subject.other | Local multiplicities |
dc.subject.other | Predistance polynomial |
dc.title | On almost distance-regular graphs |
dc.type | Article |
dc.subject.lemac | Grafs, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
dc.identifier.doi | 10.1016/j.jcta.2010.10.005 |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 4475713 |
dc.description.version | Postprint (published version) |
local.citation.author | Dalfo, C.; van Dam, E.; Fiol, M. A.; Garriga, E.; Gorissen, B. |
local.citation.publicationName | Journal of combinatorial theory. Series A |
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