Let \(G=(V(G),E(G))\) be a simple graph. A set \(S \subseteq V(G)\) is a strong edge geodetic set if there exists an assignment of exactly one shortest path between each pair of vertices from S, such that these shortest paths cover all the edges E(G). The cardinality of a smallest strong edge geodetic set is the strong edge geodetic number \(\mathrm{sg_e}(G)\) of G. In this paper, the strong edge geodetic problem is studied on the Cartesian product of two paths. The exact value of the strong edge geodetic number is computed for \(P_n \,\square \,P_2\), \(P_n \,\square \,P_3\) and \(P_n \,\square \,P_4\). Some general upper bounds for \(\mathrm{sg_e}(P_n \,\square \,P_m)\) are also proved.

令\（G =（V（G），E（G））\）为简单图形。如果\（S \ subseteq V（G）\）的集合\（S \ subseteq V（G）\）是一个强边测地集，那么在S的每对顶点之间都存在恰好一条最短路径的分配，从而这些最短路径覆盖了所有边E（G） 。最小强边测地集的基数是强边缘测地数\（\ mathrm {sg_e}（G）\）的G ^。在本文中，对两条路径的笛卡尔积进行了强边大地测量问题的研究。计算\（P_n \，\ square \，P_2 \），\（P_n \，\ square \，P_3 \）和\（P_n \，\ square \，P_4 \）。还证明了\（\ mathrm {sg_e}（P_n \，\ square \，P_m）\）的一些一般上限。