Let G be a graph with vertex set V(G). For \(u,v\in V(G)\), we write \(v\sim u\) if vertices v and u are adjacent. The Cartesian product of G and H, denoted by \(G\Box H\), is the graph with vertex set \(V(G)\times V(H)\), where \((x,u)\sim (y,v)\) if and only if \(x=y\) and \(u\sim v\) in H, or \(x\sim y\) in G and \(u=v\). The lexicographic product of G and H, denoted by G[H], is the graph with vertex set \(V(G)\times V(H)\), where \((x,u)\sim (y,v)\) if and only if \(x\sim y\) in G, or \(x=y\) and \(u\sim v\) in H. The resistance diameter of graph G refers to the maximum resistance distance among all pairs of vertices in G. Let \(P_n\) be the path of n vertices. In this paper, the resistance diameters of \(P_n\Box P_m\) and \(P_n[P_m]\) are studied. Meanwhile, the maximal resistance distance, which is among some pairs of vertices in the lexicographic product of connected graph and orderable graph, is given.

设G是一个顶点集为V ( G ) 的图。对于\(u,v\in V(G)\)，如果顶点v和u相邻，我们写\(v\sim u\)。G和H的笛卡尔积，用\(G\Box H\) 表示，是顶点集\(V(G)\times V(H)\) 的图，其中\((x,u)\sim (y,v)\)当且仅当\(x=y\)和\(u\sim v\)在H，或\(x\sim y\)在G和\(u=v\)。G的字典积和H，由G [ H ]表示，是顶点集\(V(G)\times V(H)\) 的图，其中\((x,u)\sim (y,v)\)如果和仅当\（X \ SIM Y \）中g ^，或\（X = Y \）和\（U \ SIM v \）在ħ。图的电阻直径ģ是指在所有顶点对之间的最大电阻距离ģ。设\(P_n\)为n个顶点的路径。本文中\(P_n\Box P_m\)和\(P_n[P_m]\)的电阻直径被研究。同时，给出了连通图和可排序图的字典积中一些顶点对之间的最大阻力距离。