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Paper   IPM / M / 11550
School of Mathematics
  Title:   On sum of powers of the Laplacian and signless Laplacian eigenvalues of graphs
1.  S. Akbari
2.  E. Ghorbani
3.  M. R. Oboudi (Joint with J. H. Koolen)
  Status:   Published
  Journal: Electron. J. Combin.
  Vol.:  17
  Year:  2010
  Pages:   #R115
  Supported by:  IPM
Let G be a graph of order n with signless Laplacian eigenvalues q1,...,qn and Laplacian eigenvalues μ1,...,μn. It is proved that for any real number α with 0 < α\leqslant1 or 2\leqslant α < 3, the inequality q1α+ ... + qnα\geqslant μ1α +... + μnαholds, and for any real number β with 1 < β < 2, the inequality q1β+ ...+qnβ \leqslant μ1β +...+μnβ holds. In both inequalities, the equality is attained (for α ∉ {1,2}) if and only if G is biparite.

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