Authors: Brankov, Vladimir
Hansen, Pierre
Stevanović, Dragan 
Title: Automated conjectures on upper bounds for the largest Laplacian eigenvalue of graphs
Journal: Linear Algebra and Its Applications
Volume: 414
Issue: 2-3
First page: 407
Last page: 424
Issue Date: 15-Apr-2006
Rank: M22
ISSN: 0024-3795
DOI: 10.1016/j.laa.2005.10.017
Several upper bounds on the largest Laplacian eigenvalue of a graph G, in terms of degree and average degree of neighbors of its vertices, have been proposed in the literature. We show that all these bounds, as well as many conjectured new ones, can be generated systematically using some simple algebraic manipulations. Bounds depending on the edges of G are also generated. Moreover, the interestingness of bounds is discussed, in terms of dominance and tightness. Finally, we give a unified way of proving a sample of these bounds.
Keywords: Automatic generation of conjectures | Conjecture | Graph | Laplacian eigenvalues | Laplacian matrix
Publisher: Elsevier
Project: Serbian Ministry of Science, Grant 1389
NSERC, Grant #105574–02

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