On iteration digraph and zero-divisor graph of the ring ℤn

In the first part, we assign to each positive integer n a digraph Γ(n, 5), whose set of vertices consists of elements of the ring ℤn = {0, 1, …, n − 1} with the addition and the multiplication operations modulo n, and for which there is a directed edge from a to b if and only if a5 ≡ b (mod n). Associated with Γ(n, 5) are two disjoint subdigraphs: Γ1(n, 5) and Γ2(n, 5) whose union is Γ(n, 5). The vertices of Γ1(n, 5) are coprime to n, and the vertices of Γ2(n, 5) are not coprime to n. In this part, we study the structure of Γ(n, 5) in detail.