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}
}
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. 
GRAPH COMPONENTS AND DYNAMICS OVER FINITE FIELDS
On the symmetric digraphs from powers modulo n
On the symmetric digraphs from the kth power mapping on finite commutative rings
On the heights of power digraphs modulo n
On symmetric digraphs of the congruence xk = y (mod n)

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