  We use $K$-theory to prove an isomorphism theorem for a large class of
generalised Bunce-Deddens algebras constructed by Kribs and Solel from a
directed graph $E$ and a sequence $\omega$ of positive integers. In particular,
we compute the torsion-free component of the $K_0$-group for a class of
generalised Bunce-Deddens algebras to show that supernatural numbers are a
complete invariant for this class.
