Digraphs from powers modulo \(p\). (English) Zbl 0855.05067

Lucheta, Caroline; Miller, Eli; Reiter, Clifford

Fibonacci Q. 34, No. 3, 226-239 (1996).

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 \(k\).

Reviewer: J.W.Moon (Edmonton)

MSC:

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

Keywords:

digraph; rooted trees; cycle