@article { author = {Ahmad, U. and Husnine, S‎. ‎M‎. ‎}, title = {The power digraphs of safe primes}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {42}, number = {3}, pages = {749-759}, year = {2016}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, abstract = {A power digraph, denoted by $G(n,k)$, is a directed graph with $Z_{n}={0,1,..., n-1}$ as the set of vertices and $L={(x,y):x^{k}\equiv y~(mod , n)}$ as the edge set, where $n$ and $k$ are any positive integers. In this paper, the structure of $G(2q+1,k)$, where $q$ is a Sophie Germain prime is investigated. The primality tests for the integers of the form $n=2q+1$ are established in terms of the structure of components of $G(n,k)$. The digraphs in which all components look like directed star graphs are completely classified. This work generalizes the results of M. Krizekek, L. Somer, Sophie Germain Little Suns, Math. Slovaca 54(5) (2004), 433-442.}, keywords = {Iteration digraph,Carmichael lambda function,fixed point,Sophie Germain primes,Safe primes}, url = {http://bims.iranjournals.ir/article_810.html}, eprint = {http://bims.iranjournals.ir/article_810_0df6b481f1fb0fa44a9e1d04a5d4fa1a.pdf} }