2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107680We present relations between growth, growth of diameters and the rate of vanishing of the spectral gap in Schreier graphs of automaton groups. In particular, we introduce a series of examples, called Hanoi Towers groups since they model the well known Hanoi Towers Problem, that illustrate some of the possible types of behavior.5 pagesGroup Theory20F69text