A relation between the Laplacian and signless Laplacian eigenvalues of a graph
نویسندگان
چکیده
Let G be a graph of order n such that ∑n i=0(−1)iaiλn−i and ∑n i=0(−1)ibiλn−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 q 1 + · · · + q n ≥ μα1 + · · · +μn .
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