On strong distances in oriented graphs (Q1810644)

Let \(D\) be a strongly connected digraph. The strong distance between two vertices \(u\) and \(v\) in \(D\) is the minimum size of a strongly connected subdigraph of \(D\) containing \(u\) and \(v\). The authors also define the strong connectivity, strong diameter and strong radius. The main results of the paper are: (a) estimation of the strong diameter of \(D\) using either an order and directed girth of \(D\) (Theorem 1) or an order and strong connectivity of \(D\) (Theorem 2); (b) estimation of the strong radius of \(D\).