强有向图d中任意两个点u,V的强距离Sd(u,V)定义为d中包含u和V的最小有向强子图duV的大小(弧的数目).d中一点u的强离心率SE(u)定义为u到其他顶点的强距离的最大值.强有向图d的强半径SrAd(d)(相应的强直径SdIAM(d))定义为d中所有顶点强离心率的最小值(相应的最大值).无向图g的最小定向强半径SrAd(g)(相应的最大定向强半径SrAd(g))定义为d中所有强定向的强半径的最小值(相应的最大值).无向图g的最小定向强直径SdIAM(g)(相应的最大定向强直径SdIAM(g))定义为d中所有强定向的强直径的最小值(相应的最大值).本文确定了路和路的笛卡尔积的最小定向强半径SrAd(PMxPn)和强直径的值SdIAM(PMxPn),给出了最大定向强半径SrAd(PMxPn)的界并提出关于最大定向强直径SdIAM(PMxPn)的一个猜想.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
