Minimum strong radius of the strong product of paths

Abstract

D is a strong oriented graph, the strong distance sd(u, v) is the number of arcs of D containing u and v. For a vertex v of D, the strong eccentricity se (v) is the strong distance between v and a vertex farthest from v. The strong radius srad(D) is the minimum strong eccentricity among the vertices of D. The minimum strong radius srad(G) of a graph D is the minimum strong radius over all strong orientations of G. And G1G2 denote the strong product of graphs G1 and G2 . In this paper, according to the order of paths we give the result of the minimum strong radius of the strong product of paths, and propose a new directed network design method.