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Title: Bounds for the signless laplacian energy
Author: Abreu, N.
Cardoso, Domingos M.
Gutman, I.
Martins, E. A.
Robbiano, M.
Keywords: Graph spectrum
Laplacian energy
Laplacian graph spectrum
Signless Laplacian energy
Signless Laplacian spectrum
Absolute values
Adjacency matrices
Arithmetic mean
Energy of a graph
Graph spectra
Line graph
Signless Laplacian energy
Signless Laplacian spectrum
Upper Bound
Vertex degree
Eigenvalues and eigenfunctions
Laplace transforms
Issue Date: 2011
Publisher: Elsevier
Abstract: The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. The Laplacian (respectively, the signless Laplacian) energy of G is the sum of the absolute values of the differences between the eigenvalues of the Laplacian (respectively, signless Laplacian) matrix and the arithmetic mean of the vertex degrees of the graph. In this paper, among some results which relate these energies, we point out some bounds to them using the energy of the line graph of G. Most of these bounds are valid for both energies, Laplacian and signless Laplacian. However, we present two new upper bounds on the signless Laplacian which are not upper bounds for the Laplacian energy. © 2010 Elsevier Inc. All rights reserved.
Peer review: yes
ISSN: 0024-3795
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Appears in Collections:DMat - Artigos

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