## “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.