  The derived graph of a voltage graph consisting of a single vertex and two
loops of different voltages is a circulant graph with two generators. We
characterize the automorphism groups of connected, two-generator circulant
graphs, and give their determining and distinguishing number, and when
relevant, their cost of 2-distinguishing. We do the same for the subdivisions
of connected, two-generator circulant graphs obtained by replacing one loop in
the voltage graph with a directed cycle.
