  We establish conditions for a permutation group generated by a single
permutation of a prime power order to be an automorphism group of a graph or an
edge-colored graph. This corrects and generalizes the results of the two papers
on cyclic permutation groups published in 1978 and 1981 by S. P. Mohanty, M. R.
Sridharan, and S. K. Shukla.
