The Structure of Isomorphic Digraph from Powers Modulo pe

Abstract

For positive integers n and k, let G(n,k) denote the digraph whose set of vertices is {0,1,2,…,n-1} and there is a directed edge from a to b if ak≡b  (mod n). It is great value to consider conditions of G(p,k1)≃G(p,k2). In this paper, we obtain necessary and sufficient conditions for G(n,k1)≃G(n,k2) when n=pe.