## 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