139 research outputs found
Sharp Bounds for the Signless Laplacian Spectral Radius in Terms of Clique Number
In this paper, we present a sharp upper and lower bounds for the signless
Laplacian spectral radius of graphs in terms of clique number. Moreover, the
extremal graphs which attain the upper and lower bounds are characterized. In
addition, these results disprove the two conjectures on the signless Laplacian
spectral radius in [P. Hansen and C. Lucas, Bounds and conjectures for the
signless Laplacian index of graphs, Linear Algebra Appl., 432(2010) 3319-3336].Comment: 15 pages 1 figure; linear algebra and its applications 201
A Sharp upper bound for the spectral radius of a nonnegative matrix and applications
In this paper, we obtain a sharp upper bound for the spectral radius of a
nonnegative matrix. This result is used to present upper bounds for the
adjacency spectral radius, the Laplacian spectral radius, the signless
Laplacian spectral radius, the distance spectral radius, the distance Laplacian
spectral radius, the distance signless Laplacian spectral radius of a graph or
a digraph. These results are new or generalize some known results.Comment: 16 pages in Czechoslovak Math. J., 2016. arXiv admin note: text
overlap with arXiv:1507.0705
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