On sum of powers of the Laplacian eigenvalues of graphs
نویسندگان
چکیده
منابع مشابه
On Sum of Powers of the Laplacian and Signless Laplacian Eigenvalues of Graphs
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 6 1 or 2 6 α < 3, the inequality qα 1 + · · · + qα n > μ1 + · · · + μn holds, and for any real number β with 1 < β < 2, the inequality q 1 + · · ·+ q n 6 μβ1 + · · ·+ μ β n holds. In both inequalities, the equality is attaine...
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For a graph G and a real α / = 0, we study the graph invariant sα(G) – the sum of the αth power of the non-zero Laplacian eigenvalues of G. The cases α = 2, 1 2 and −1 have appeared in different problems. Here we establish some properties for sα with α / = 0, 1. We also discuss the cases α = 2, 1 2 . © 2008 Elsevier Inc. All rights reserved. AMS classification: 05C50; 05C90
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For a graph G without isolated vertices and a real α = 0, we introduce a new graph invariant s∗α (G)the sum of the αth power of the non-zero normalized Laplacian eigenvalues of G. Recently, the cases α = 2 and −1 have appeared in various problems in the literature. Here, we present some lower and upper bounds of s∗α (G) for a connected graph G, where α = 0, 1. We also discuss the case α = −1.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2008
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.06.023