Lower and Upper Orientable Strong Radius and Diameter of Cartesian Product of Paths
Meirun Chen · Shinjang dashösi ilmiy jurnili · 2009
For two vertices u and v in a strong digraph D,the strong distance sd(u,v)between u and v is the minimum size(the number of arcs)of a strong sub-digraph 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)(resp.strong diameter sdiam(D))is the minimum(resp.maximum)strong eccentricity among the vertices of D.The lower(resp.upper)orientable strong radius srad(G)(resp.SRAD(G))of a graph G is the minimum(resp.maximum)strong radius over all strong orientations of G.The lower(resp.upper) orientable strong diameter sdiam(G)(resp.SDIAM(G))of a graph G is the minimum(resp.maximum) strong diameter over all strong orientations of G.In this paper,we determine the lower orientable strong radius and strong diameter of Cartesian product of paths,and give bounds on the upper orientable strong radius and a conjecture of the upper orientable strong diameter of Cartesian product of paths.