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 \(k = 4\).


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


GAP; Graphviz
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