We describe the functional graph of the multiplication-by-n map in a cycle group and use this
to obtain the structure of the functional graph associated with a Rédei function over a …

For a finite commutative ring $ S $(resp., a finite abelian group $ S $) and a positive integer
$ k\geqslant2 $, we construct an iteration digraph $ G (S, k) $ whose vertex set is $ S $ and …

The power graph of a semigroup S is a simple graph with vertex set S and two distinct
vertices x and y are adjacent if and only if xm= y or ym= x for some positive integer m. If m is …

We attach a diagraph with generalized Quaternion group of order 4 n by utilizing the power
map f: Q 4 n→ Q 4 n defined by f (x)= xk for all x∈ Q 4 n, where k is a fixed natural number …

Vasiga and Shallit [17] study tails and cycles in orbits of iterations of quadratic polynomials
over prime fields. These results were extended to repeated exponentiation by Chou and …

Let X be a group and k≥ 2 be a positive integer. The k-power digraph G (X, k) is consisting
of vertex set X and there is a directed edge from x to y if and only if xk= y. We study the k …

Aiming at a better understanding of finite groups as finite dynamical systems, we show that
by a version of Fitting's Lemma for groups, each state space of an endomorphism of a finite …