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Power digraphs modulo \(n\). (English) Zbl 0936.05049

Suppose a digraph has vertices labeled \(1,2,\dots, n\) and with an edge from vertex \(b_1\) to \(b_2\) if \(f(b_1)= b_2\pmod n\) for any function \(f\) modulo \(n\). The author studies digraphs resulting from the function \(f(x)= x^k\) for arbitrary \(n\). In particular, cycles, trees and structural properties of the associated digraphs are investigated.

MSC:

05C20 Directed graphs (digraphs), tournaments
11B50 Sequences (mod \(m\))

Keywords:

digraph; cycles; trees
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