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Title: Upper bounds on the Laplacian energy of some graphs
Author: Robbiano, M.
Martins, E. A.
Jiménez, R.
Martín, B. S.
Keywords: Laplacian matrix
Bethe tree
Laplacian energy
Issue Date: 2010
Publisher: University of Kragujevac
Abstract: The Laplacian energy L£[G] of a simple graph G with n vertices and m edges is equal to the sum of distances of the Laplacian eigenvalues to their average. For 1 ≤ j ≤ s, let Aj be matrices of orders n j. Suppose that det(L(G) - λIn) = Πj=1s det(Aj- - λI n,j)tj, with tj > 0. In the present paper we prove LE[G) ≤ Σ j=1stj√n j||Aj-2m/n||F≤ √n||L(G) - 2m/nIn||F , where ||·||F stands for the Frobenius matrix norm.
Peer review: yes
ISSN: 0340-6253
Appears in Collections:DMat - Artigos

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