Structure of digraphs associated with quadratic congruences with composite moduli

@article{Somer2006StructureOD,
  title={Structure of digraphs associated with quadratic congruences with composite moduli},
  author={Lawrence Somer and Michal Kr{\'i}zek},
  journal={Discret. Math.},
  year={2006},
  volume={306},
  pages={2174-2185}
}
We assign to each positive integer n a digraph G(n) whose set of vertices is H={0,1,...,n-1} and for which there exists a directed edge from a@?H to b@?H if a^2=b(modn). Associated with G(n) are two disjoint subdigraphs: G"1(n) and G"2(n) whose union is G(n). The vertices of G"1(n) correspond to those residues which are relatively prime to n. The structure of G"1(n) is well understood. In this paper, we investigate in detail the structure of G"2(n). 
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