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

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      Author
      Yıldırım, E. A.
      Date
      2010
      Source Title
      Mathematical Methods of Operations Research
      Print ISSN
      1432-2994
      Electronic ISSN
      1432-5217
      Publisher
      Springer
      Volume
      71
      Issue
      2
      Pages
      267 - 281
      Language
      English
      Type
      Article
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      Abstract
      Given 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.
      Keywords
      Maximum clique
      Maximum stable set
      Stability number
      Clique number
      Graph spectra
      Permalink
      http://hdl.handle.net/11693/22376
      Published Version (Please cite this version)
      http://dx.doi.org/10.1007/s00186-009-0295-4
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