A simpler characterization of a spectral lower bound on the clique number

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dc.citation.epage281en_US
dc.citation.issueNumber2en_US
dc.citation.spage267en_US
dc.citation.volumeNumber71en_US
dc.contributor.authorYıldırım, E. A.en_US
dc.date.accessioned2016-02-08T09:59:18Z
dc.date.available2016-02-08T09:59:18Z
dc.date.issued2010en_US
dc.departmentDepartment of Industrial Engineeringen_US
dc.description.abstractGiven a simple, undirected graph G, Budinich (Discret Appl Math 127:535-543, 2003) proposed a lower bound on the clique number of G by combining the quadratic programming formulation of the clique number due to Motzkin and Straus (Can J Math 17:533-540, 1965) with the spectral decomposition of the adjacency matrix of G. This lower bound improves the previously known spectral lower bounds on the clique number that rely on the Motzkin-Straus formulation. In this paper, we give a simpler, alternative characterization of this lower bound. For regular graphs, this simpler characterization allows us to obtain a simple, closed-form expression of this lower bound as a function of the positive eigenvalues of the adjacency matrix. Our computational results shed light on the quality of this lower bound in comparison with the other spectral lower bounds on the clique number.en_US
dc.identifier.doi10.1007/s00186-009-0295-4en_US
dc.identifier.eissn1432-5217
dc.identifier.issn1432-2994
dc.identifier.urihttp://hdl.handle.net/11693/22376
dc.language.isoEnglishen_US
dc.publisherSpringeren_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s00186-009-0295-4en_US
dc.source.titleMathematical Methods of Operations Researchen_US
dc.subjectMaximum cliqueen_US
dc.subjectMaximum stable seten_US
dc.subjectStability numberen_US
dc.subjectClique numberen_US
dc.subjectGraph spectraen_US
dc.titleA simpler characterization of a spectral lower bound on the clique numberen_US
dc.typeArticleen_US
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