Bounds on the spectral radius of nonnegative matrices and applications in graph spectra

2013/10/20 by Shu‐Yu Cui, Cui, Shu-Yu, Gui‐Xian Tian +1
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1310.5292

openalex publication_date 2013/10/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we give upper and lower bounds for the spectral radius of a nonnegative irreducible matrix and characterize the equality cases. These bounds theoretically improve and generalize some known results of Duan et al.[X. Duan, B. Zhou, Sharp bounds on the spectral radius of a nonnegative matrix, Linear Algebra Appl. (2013), http://dx.doi.org/10.1016/j.laa.2013.08.026]. Finally, applying these bounds to various matrices associated with a graph, we obtain some new upper and lower bounds on various spectral radiuses of graphs, which generalize and improve some known results.

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