Authors: Stevanović, Dragan 
Title: Large sets of noncospectral graphs with equal laplacian energy
Journal: Match
Volume: 61
Issue: 2
First page: 463
Last page: 470
Issue Date: 22-Jun-2009
Rank: M21a
ISSN: 0340-6253
Several alternative definitions to graph energy have appeared in literature recently, the first among them being the Laplacian energy, defined by Gutman and Zhou in [Linear Algebra Appl. 414 (2006), 29-37]. We show here that Laplacian energy apparently has small power of discrimination among threshold graphs, by showing that, for each n, there exists a set of n mutually noncospectral connected threshold graphs with equal Laplacian energy with O(√n) vertices only. Nevertheless, situation becomes opposite when trees are considered, as it turns out that, up to 20 vertices, there exists no pair of noncospectral trees with equal Laplacian energies.
Publisher: Faculty of Sciences, University of Kragujevac
Project: Slovenian Agency for Research, program P1-0285
Serbian Ministry of Science, research grant 144015G

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