On symmetries of power digraphs

Abstract

An iteration directed graph whose set of vertices is {0,l,⋯,n-1} and whose setof edges is{(a,b) : a^k = b(modn)} is denoted by G(n, k). It is called symmetric of order m if we can partition G(n, k) into subdigraphs, each containing m isomorphic components. In this paper we extend the results given by Kramer-Miller in [1] and by Somer in [2] by finding necessary and sufficient conditions for G(n, k) to be symmetric of order p where n = pαq1⋯q_m and p , q_i are odd prime divisors of n and α > 1.