On strong distances in oriented graphs

Let D be a strongly connected digraph. The strong distance between two vertices u and v in D, denoted by sd _D(u,v) is the minimum size of a strongly connected subdigraph of D containing u and v. The strong eccentricity, se(u), of a vertex u of D, is the strong distance between u and a vertex farthest from u. The minimum strong eccentricity among the vertices of D is the strong radius, srad(D), and the maximum strong eccentricity is the strong diameter, sdiam(D). For asymmetric digraphs (that is, oriented graphs) we present bounds on the strong radius in terms of order and on the strong diameter in terms of order, girth and connectivity.