Applications of the Gauge-invariant uniqueness theorem for graph algebras

We give applications of the gauge-invariant uniqueness theorem, which states that the Cuntz-Krieger algebras of directed graphs are characterised by the existence of a canonical action of . We classify theC*-algebras of higher order graphs, identify theC*-algebras of cartesian product graphs with a certain fixed point algebra and investigate a relation called elementary shift equivalence on graphs and its effect on the associated graphC*-algebras.