The classification of some generalised Bunce-Deddens algebras

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 ω of positive integers. In particular, we compute the torsion-free component of the K0-group for a class of generalised Bunce-Deddens algebras to show that supernatural numbers are a complete invariant for this class.