A sharp upper bound for the spectral radius of a nonnegative matrix and applications

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, t...

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Bibliographic Details
Published inCzechoslovak mathematical journal Vol. 66; no. 3; pp. 701 - 715
Main Authors You, Lihua, Shu, Yujie, Zhang, Xiao-Dong
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2016
Springer Nature B.V
Subjects
Analysis
Convex and Discrete Geometry
Graph theory
Input output
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Spectra
Upper bounds
spectral radius
05C50
nonnegative matrix
digraph
graph
15A18
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Summary: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 an undirected graph or a digraph. These results are new or generalize some known results.
ISSN:0011-4642
1572-9141
DOI:10.1007/s10587-016-0287-5