  Quantum isometry groups of spectral triples associated with approximately
finite-dimensional C*-algebras are shown to arise as inductive limits of
quantum symmetry groups of corresponding truncated Bratteli diagrams. This is
used to determine explicitly the quantum isometry group of the natural spectral
triple on the algebra of continuous functions on the middlethird Cantor set. It
is also shown that the quantum symmetry groups of finite graphs or metric
spaces coincide with the quantum isometry groups of the corresponding classical
objects equipped with natural Laplacians.
