On the symmetric digraphs from powers modulo n

@article{Deng2012OnTS,
  title={On the symmetric digraphs from powers modulo n},
  author={Guixin Deng and Pingzhi Yuan},
  journal={Discret. Math.},
  year={2012},
  volume={312},
  pages={720-728}
}
For any positive integers n and k, let G(n,k) denote the digraph whose set of vertices is H={0,1,2,...,n-1} and there is a directed edge from a@?H to b@?H if a^k=b(modn). The digraph G(n,k) is called symmetric of order M if its set of connected components can be partitioned into subsets of size M with each subset containing M isomorphic components. In this paper, we establish a necessary and sufficient condition for G(n,k) to be symmetric of order M, where M has an odd prime divisor. 

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