The structure of power digraph connected with the congruence a¹¹ ≡ b(mod n)

We assign to each positive integer n a digraph Γ(n, 11) whose set of vertices is Zn = {0, 1, 2, ..., − 1} and there exists exactly one directed edge from b if only a11 ≡ b(mod n), where a, ∈ Zn. Let Γ1(n, be the subdigraph induced by which are coprime n. discuss when regular or semi-regular. A formula for number fixed points established. necessary sufficient condition symmetry proved. Moreover, using Carmichael ́s lambda function, components conditions existence cycles in presented.