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Carlip, Walter; Mincheva, Martina

Symmetry of iteration graphs. (English) Zbl 1174.05048

Czech. Math. J. 58, No. 1, 131-145 (2008).
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 \(k = 4\).

Cited in 9 Documents

MSC:

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

Keywords:

digraph; iteration digraph; quadratic map; tree; cycle

Software:

Graphviz; GAP
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\textit{W. Carlip} and \textit{M. Mincheva}, Czech. Math. J. 58, No. 1, 131--145 (2008; Zbl 1174.05048)
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References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.