## “School of Mathematics”

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Paper   IPM / M / 9554
School of Mathematics
Title:   On the sum of Laplacian eigenvalues of graphs
Author(s):
 1 A. Mohammadian 2 B. Tayfeh-Rezaie (Joint with W. H. Haemers)
Status:   Published
Journal: Linear Algebra Appl.
Vol.:  432
Year:  2010
Pages:   2214-2221
Supported by:  IPM
Abstract:
Let k be a natural number and let G be a graph with at least k vertices. A.E. Brouwer conjectured that the sum of the k largest Laplacian eigenvalues of G is at most e(G)+((k+1) || 2), where e(G) is the number of edges of G. We prove this conjecture for k=2. We also show that if G is a tree, then the sum of the k largest Laplacian eigenvalues of G is at most e(G)+2k−1.

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