A matrix realization of spectral bounds

2023/07/08 by Yen-Jen Cheng, Cheng, Yen-Jen, Chih-wen Weng +1 · 2 citations
Computer Science · Engineering · Mathematics · #05C50 #15A42 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2307.03880

openalex publication_date 2023/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We give a unified and systematic way to find bounds for the largest real eigenvalue of a nonnegative matrix by considering its modified quotient matrix. We leverage this insight to identify the unique class of matrices whose largest real eigenvalue is maximum among all (0,1)-matrices with a specified number of ones. This result resolves a problem that was posed independently by R. Brualdi and A. Hoffman, as well as F. Friedland, back in 1985.

Cited by

• A new spectral Turán theorem for weighted graphs and consequences
• Nordhaus-Gaddum inequality for the spectral radius of a graph of order n

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