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dc.contributor.authorFiol Mora, Miquel Àngel
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.date.accessioned2012-01-23T10:48:39Z
dc.date.available2012-01-23T10:48:39Z
dc.date.created1999-03
dc.date.issued1999-03
dc.identifier.citationFiol, M. A. Eigenvalue interlacing and weight parameters of graphs. "Linear algebra and its applications", Març 1999, vol. 290, p. 275-301.
dc.identifier.issn0024-3795
dc.identifier.urihttp://hdl.handle.net/2117/14729
dc.description.abstractEigenvalue interlacing is a versatile technique for deriving results in algebraic combinatorics. In particular, it has been successfully used for proving a number of results about the relation between the (adjacency matrix or Laplacian) spectrum of a graph and some of its properties. For instance, some characterizations of regular partitions, and bounds for some parameters, such as the independence and chromatic numbers, the diameter, the bandwidth, etc., have been obtained. For each parameter of a graph involving the cardinality of some vertex sets, we can define its corresponding weight parameter by giving some "weights" (that is, the entries of the positive eigenvector) to the vertices and replacing cardinalities by square norms. The key point is that such weights "regularize" the graph, and hence allow us to define a kind of regular partition, called "pseudo-regular," intended for general graphs. Here we s~aow how to use interlacing for proving results about some weight parameters and pseudo-regular partitions of a graph. For instance, generalizing a well-known result of Lovfisz, it is shown that the weight Shannon capacity 6)* of a connected graph F, with n vertices and (adjacency matrix) eigenvalues 2j > )~2 ~> '" ~> 2,, satisfies o~<o*~< Ilvll 1 -- ; - l / " ; - n 'where O is the (standard) Shannon capacity and v is the positive eigenvector normalized to have smallest entry 1. In the special case of regular graphs, the results obtained have some interesting corollaries, such as an upper bound for some of the multiplicities of the eigenvalues of a distance-regular graph. Finally, some results involving the Laplacian spectrum are derived.
dc.format.extent27 p.
dc.language.isoeng
dc.publisherElsevier
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
dc.subject.lcshGraph theory
dc.titleEigenvalue interlacing and weight parameters of graphs
dc.typeArticle
dc.subject.lemacGrafs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.description.peerreviewedPeer Reviewed
dc.subject.ams05C Teoria de grafs
dc.relation.publisherversionhttp://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V0R-3WKXS2G-M&_user=1517299&_coverDate=03%2F15%2F1999&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_acct=C000053450&_version=1&_urlVersion=0&_userid=1517299&md5=bde58bab55b6d6cacba67e1f178c13b1&searchtype=a
dc.rights.accessOpen Access
local.identifier.drac774537
dc.description.versionPostprint (published version)
local.citation.authorFiol, M. A.
local.citation.publicationNameLinear algebra and its applications
local.citation.volume290
local.citation.startingPage275
local.citation.endingPage301


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