The hull number of an oriented graph

Abstract

We present characterizations of connected graphs G of order n≥2 for which h+(G)=n. It is shown that for every two integers n and m with 1≤n−1≤m≤(n2), there exists a connected graph G of order n and size m such that for each integer k with 2≤k≤n, there exists an orientation of G with hull number G.