Highly irregular digraphs (Q686429)

A graph \(G\) is highly irregular if for each vertex \(v\) of \(G\) no two vertices adjacent with \(v\) have the same degree in \(G\). The authors extend this concept to digraphs as follows: A digraph \(D\) is highly irregular if for every vertex \(v\) of \(D\) no two vertices in the out neighbourhood of \(v\) have the same out degree in \(D\). The authors extend several of the results that are known for highly irregular graphs to highly irregular digraphs.