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 T. We classify the C*-algebras of higher order graphs, identify the C*-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 graph C*-algebras.