The minimum exponent of the primitive digraphs on the given number of arcs

Abstract

Primitive digraphs on \(n\) vertices, \(k\) arcs and girth \(s\) are considered. By \(a(n,k,s)\) we mean the minimum exponent taken over all such digraphs. We estimate the number \(a(n,k,s)\) using the Frobenius number for special values of \(k\) and \(s\).

Keywords

• primitive directed graph
• exponent
• Frobenius number