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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, 1/2) there exists a positive number τ₂(α)>2 such that any value λ> τ₂(α) is an Aα-limit point. We also determine the existence of other intervals for which all its points are Aα-limit points.
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Oliveira et al. (2024) studied this question.
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