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