# Symmetry of iteration graphs

```@article{Carlip2008SymmetryOI,
title={Symmetry of iteration graphs},
author={Walter Carlip and Martina Mincheva},
journal={Czechoslovak Mathematical Journal},
year={2008},
volume={58},
pages={131-145}
}```
• Published 2008
• Mathematics
• Czechoslovak Mathematical Journal
We examine iteration graphs of the squaring function on the rings ℤ/nℤ when n = 2kp, for p a Fermat prime. We describe several invariants associated to these graphs and use them to prove that the graphs are not symmetric when k = 3 and when k ⩾ 5 and are symmetric when k = 4.
9 Citations
GRAPH COMPONENTS AND DYNAMICS OVER FINITE FIELDS
• Mathematics
• 2014
For polynomials and rational maps of fixed degree over a finite field, we bound both the average number of components of their functional graphs as well as the average number of periodic points ofExpand
Symmetric Digraphs from Powers Modulo n
• Mathematics
• 2011
For each pair of positive integers n and k, let G(n,k) denote the digraph whose set of vertices is H = {0,1,2,···, n – 1} and there is a directed edge from a ∈ H to b ∈ H if a ≡ b(mod n). The digraphExpand
The structure of digraphs associated with the congruence xk ≡ y (mod n)
• Mathematics
• 2011
We assign to each pair of positive integers n and k ⩾ 2 a digraph G(n, k) whose set of vertices is H = {0, 1, ..., n − 1} and for which there is a directed edge from a ∈ H to b ∈ H if ak ≡ b (mod n).Expand
On the symmetric digraphs from powers modulo n
• Computer Science, Mathematics
• Discret. Math.
• 2012
This paper establishes a necessary and sufficient condition for G(n,k) to be symmetric of order M, where M has an odd prime divisor. Expand
On the symmetric digraphs from the kth power mapping on finite commutative rings
• Mathematics, Computer Science
• Discret. Math. Algorithms Appl.
• 2015
If the characteristic of R is a prime p, the digraph G(R, k) is called symmetric of order M if its set of connected components can be partitioned into subsets of size M with each subset containing M isomorphic components. Expand
On the heights of power digraphs modulo n
• Mathematics
• 2012
A power digraph, denoted by G(n, k), is a directed graph with ℤn = {0, 1, &h., n − 1} as the set of vertices and E = {(a, b): ak ≡ b (mod n)} as the edge set. In this paper we extend the work done byExpand
On symmetric digraphs of the congruence xk = y (mod n)
• Computer Science, Mathematics
• Discret. Math.
• 2009
This work generalizes earlier theorems by Szalay, Carlip, and Mincheva on symmetric digraphs G(n,2) of order 2 to symmetricDigraphs M of order M when k>=2 is arbitrary. Expand
A probabilistic heuristic for counting components of functional graphs of polynomials over finite fields
• Mathematics
• 2016
In 2014, Flynn and the second author bounded the average number of components of the functional graphs of polynomials of fixed degree over a finite field. When the fixed degree was large (relative toExpand

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