Journal
DISCRETE MATHEMATICS
Volume 310, Issue 21, Pages 2858-2866Publisher
ELSEVIER
DOI: 10.1016/j.disc.2010.06.030
Keywords
Signless Laplacian; Largest eigenvalue; Cospectral graphs; Graph index; Spectral characterization; Friendship graph
Categories
Funding
- NSFC [10961023]
- XGEDU [2009 S20]
- PRIN (Italy)
- Serbian Ministry for Science [144015G]
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In this paper, we first give an upper bound for the largest signless Laplacian eigenvalue of a graph and find all the extremal graphs. Secondly, we consider the second-largest signless Laplacian eigenvalue and we characterize the connected graphs whose second-largest signless Laplacian eigenvalue does not exceed 3. Furthermore, we give the signless Laplacian spectral characterization of the latter graphs. in particular, the well-known friendship graph is proved to be determined by the signless Laplacian spectrum. (C) 2010 Elsevier B.V. All rights reserved.
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