The power digraphs of finite groups

Abstract

An iteration directed graph whose set of vertices is a finite group of order n and whose set of edges is {(a, 6) : A^k = 6Va,6 6 0} is called a power digraph and denoted by γG(n, k). In this paper, we establish the necessary and sufficient conditions for k) to be symmetric of order p, where G is a cyclic group of order n and p | n. We also extend some of the results on cycles and in-degrees of vertices given in Min Sha, digraphs from endomorphisms of finite cyclic groups, Journal of combinatorial mathematics and combinatorial computing 83 (2012), 105-120. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.