Limit points of Aα-matrices of graphs

We study limit points of the spectral radii of Aα-matrices of graphs. Adapting a method used by J. B. Shearer in 1989, we prove a density property of Aα-limit points of caterpillars for α close to zero. Precisely, we show that for α∈[0,12) there exists a positive number τ2(α)>2 such that any valu...

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Bibliographic Details
Published in:Linear algebra and its applications Vol. 728; pp. 1 - 25
Main Authors: Oliveira, Elismar R., Trevisan, Vilmar
Format: Journal Article
Language:English
Published: Elsevier Inc 01.01.2026
Subjects:
Limit points
Spectral radius
Tree
Tree
05C50
Limit points
Spectral radius
05C05
15A18
ISSN:0024-3795
Online Access:Get full text
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Summary:We study limit points of the spectral radii of Aα-matrices of graphs. Adapting a method used by J. B. Shearer in 1989, we prove a density property of Aα-limit points of caterpillars for α close to zero. Precisely, we show that for α∈[0,12) there exists a positive number τ2(α)>2 such that any value λ>τ2(α) is an Aα-limit point. We also determine other intervals whose numbers are all Aα-limit points.
ISSN:0024-3795
DOI:10.1016/j.laa.2025.08.014