Graphical Cyclic Permutation Groups

TL;DR

This paper characterizes when permutation groups generated by a prime power order permutation can serve as automorphism groups of graphs or edge-colored graphs, correcting and extending earlier results from the late 1970s and early 1980s.

Contribution

It provides new conditions for such permutation groups to be automorphism groups, generalizing previous findings and correcting earlier inaccuracies.

Findings

Established conditions for automorphism groups generated by prime power order permutations.

Corrected and extended previous results from 1978 and 1981.

Generalized the characterization to broader classes of graphs.

Abstract

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.