## Digraphs from powers modulo $$p$$.(English)Zbl 0855.05067

Let $$G^k_p$$ denote the digraph whose vertices are the nonzero residues modulo the prime $$p$$ in which there is an edge directed from vertex $$a$$ to vertex $$b$$ if and only if $$a^k\equiv b\pmod p$$; each component of such a graph consists of a collection of rooted trees whose roots lie on a cycle. The authors describe a number of graph-theoretical features of $$G^k_p$$ that can be determined in terms of number-theoretical properties of $$p$$ and $$k$$.

### MSC:

 05C20 Directed graphs (digraphs), tournaments 11B50 Sequences (mod $$m$$) 05C38 Paths and cycles

### Keywords:

digraph; rooted trees; cycle