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IPM
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“School of Mathematics”

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Paper   IPM / M / 11481
School of Mathematics
  Title:   A relation between the Laplacian and signless Laplacian eigenvalues of a graph
  Author(s): 
1.  S. Akbari
2.  E. Ghorbani
3.  M. R. Oboudi (Joint with J. H. Koolen)
  Status:   Published
  Journal: J. Algebraic Combin.
  Vol.:  32
  Year:  2010
  Pages:   459-464
  Supported by:  IPM
  Abstract:
Let G be a graph of order n such that ∑i=0n (−1)i aiλni and ∑i=0n (−1)i bi λni are the characteristic polynomials of the signless Laplacian and the Laplacian matrices of G, respectively. We show that aibi for i=0,1,...,n. As a consequence, we prove that for any α,0 < α ≤ 1, if q1,...,qn and μ1,...,μn are the signless Laplacian and the Laplacian eigenvalues of G, respectively, then q1α+...+qnα ≥ μ1α+...+μnα.

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