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|Paper IPM / M / 11481||
Let G be a graph of order n such that ∑i=0n (−1)i aiλn−i and ∑i=0n (−1)i bi λn−i are the characteristic polynomials of the signless Laplacian and the Laplacian matrices of G, respectively. We show that ai ≥ bi 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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