We explore the recently introduced local-triviality dimensions by studying gauge actions on graph C*-algebras, as well as the restrictions of the gauge action to finite cyclic subgroups. For C*-algebras of finite acyclic graphs and finite cycles, we characterize the finiteness of these dimensions, and we further study the gauge actions on many examples of graph C*-algebras. These include the Toeplitz algebra, Cuntz algebras, and q-deformed spheres. This is joint work with A. Chirvasitu and B. Passer.