THE POWER DIGRAPHS OF FINITE GROUPS

摘要

An iteration directed graph whose set of vertices is a finite group of order n and whose set of edges is {(a,b) : a(k) = b for all a, b is an element of G} is called a power digraph and denoted by gamma G(n, k). In this paper, we establish the necessary and sufficient conditions for gamma G (n, k) to be symmetric of order p, where G is a cyclic group of order n and p vertical bar 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.