Structure of digraphs associated with quadratic congruences with composite moduli

We assign to each positive integer n   a digraph G(n)G(n) whose set of vertices is H={0,1,…,n-1}H={0,1,…,n-1} and for which there exists a directed edge from a∈Ha∈H to b∈Hb∈H if a2≡b(modn). Associated with G(n)G(n) are two disjoint subdigraphs: G1(n)G1(n) and G2(n)G2(n) whose union is G(n)G(n). The vertices of G1(n)G1(n) correspond to those residues which are relatively prime to n  . The structure of G1(n)G1(n) is well understood. In this paper, we investigate in detail the structure of G2(n)G2(n).