## Symmetry of iteration graphs.(English)Zbl 1174.05048

Summary: We examine iteration graphs of the squaring function on the rings $$\mathbb Z/n\mathbb Z$$ when $$n = 2^{k}p$$, for $$p$$ a Fermat prime. We describe several invariants associated with these graphs and use them to prove that the graphs are not symmetric when $$k = 3$$ and when $$k \geq 5$$ and are symmetric when $$k = 4$$.

### MSC:

 05C20 Directed graphs (digraphs), tournaments 11T99 Finite fields and commutative rings (number-theoretic aspects)

### Keywords:

digraph; iteration digraph; quadratic map; tree; cycle

GAP; Graphviz
Full Text:

### References:

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