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Please use this identifier to cite or link to this item: https://www.um.edu.mt/library/oar/handle/123456789/28154
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dc.contributor.authorCardoso, Domingos M.-
dc.contributor.authorSciriha, Irene-
dc.contributor.authorZerafa, Cheryl-
dc.date.accessioned2018-03-22T12:53:19Z-
dc.date.available2018-03-22T12:53:19Z-
dc.date.issued2010-
dc.identifier.citationCardoso, D. M., Sciriha, I., & Zerafa, C. (2010). Main eigenvalues and (κ, τ)-regular sets. Linear Algebra and its Applications, 432(9), 2399-2408.en_GB
dc.identifier.urihttps://www.um.edu.mt/library/oar//handle/123456789/28154-
dc.description.abstractA (κ, τ)-regular set is a subset of the vertices of a graph , inducing a κ-regular subgraph such that every vertex not in the subset has τ neighbors in it. A main eigenvalue of the adjacency matrix A of a graph has an eigenvector not orthogonal to the all-one vector j. For graphs with a (κ, τ)-regular set a necessary and sufficient condition for an eigenvalue be non-main is deduced and the main eigenvalues are characterized. These results are applied to the construction of infinite families of bidegreed graphs with two main eigenvalues and the same spectral radius (index) and some relations with strongly regular graphs are obtained. Finally, the determination of (κ, τ)-regular sets is analyzed.en_GB
dc.language.isoenen_GB
dc.publisherElsevier BVen_GB
dc.rightsinfo:eu-repo/semantics/restrictedAccessen_GB
dc.subjectEigenvaluesen_GB
dc.subjectMathematics -- Charts, diagrams, etc.en_GB
dc.subjectMathematics -- Problems, exercises, etc.en_GB
dc.titleMain eigenvalues and (κ, τ)-regular setsen_GB
dc.typearticleen_GB
dc.rights.holderThe copyright of this work belongs to the author(s)/publisher. The rights of this work are as defined by the appropriate Copyright Legislation or as modified by any successive legislation. Users may access this work and can make use of the information contained in accordance with the Copyright Legislation provided that the author must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the prior permission of the copyright holder.en_GB
dc.description.reviewedpeer-revieweden_GB
dc.identifier.doi10.1016/j.laa.2009.07.039-
dc.publication.titleLinear Algebra and its Applicationsen_GB
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