In this presentation, I will discuss joint work with Teresa Bates and David Pask concerning (discrete) group actions on labeled graphs and the resulting crossed product C*-algebras. In particular, I will discuss a version of the Gross-Tucker Theorem for labeled graphs.

A labeled graph (E,L) over an alphabet A consists of a directed graph E together with a labeling map L : E¹ -> A. One can associate a C*-algebra to a labeled graph (E,L) in such a way that if the labeling L is trivial then the resulting C*-algebra is the C*-algebra of the graph E. Further, just as there is a canonical correspondence between graph C*-algebras and shifts of finite type, there is a similar correspondence between the C*-algebras of labeled and sophic shifts.