Limit points of A_α-matrices of graphs

2024/04/16 by Elismar R. Oliveira, Oliveira, Elismar R., Vilmar Trevisan +1
Computer Science · Engineering · Mathematics · #05C05 #05C50 #15A18 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory (math.SP) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2404.10953

openalex publication_date 2024/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study limit points of the spectral radii of A_α-matrices of graphs. Adapting a method used by J. B. Shearer in 1989, we prove a density property of A_α-limit points of caterpillars for α close to zero. Precisely, we show that for α∈ [0, 1/2) there exists a positive number τ₂(α)>2 such that any value λ> τ₂(α) is an A_α-limit point. We also determine the existence of other intervals for which all its points are A_α-limit points.

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