Journal
LINEAR ALGEBRA AND ITS APPLICATIONS
Volume 438, Issue 3, Pages 1215-1222Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.laa.2012.07.052
Keywords
Signless laplacian; Second largest eigenvalue; Eigenvalue bounds
Categories
Funding
- CNPq [201888/2010-6]
- NSF [DMS-0906634]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0906634] Funding Source: National Science Foundation
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Let G be a graph of order n, and let q(1) (G) >= ... >= q(n) (G) be the eigenvalues of the Q-matrix of C. also known as the signless Laplacian of G. We give a necessary and sufficient condition for the equality q(k) (G) = n - 2, where 1 < k <= n. In particular, this result solves an open problem raised by Wang, Belardo, Huang and Borovicanin. We also show that q(2) (G) >= delta (G) and determine all graphs for which equality holds. (C) 2012 Elsevier Inc. All rights reserved.
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