Monitoring-edge-geodetic sets in product networks

Let G be a graph with vertex set V(G) and edge set E(G). For any e∈E(G) and u,v∈V(G), the edge e is monitored by two vertices u and v in graph G if dG(u,v)≠dG−e(u,v). A set M of vertices of G is a monitoring-edge-geodetic set of G if for any edge e∈E(G) there exists a pair u,v∈M such that e is monitored by u, v. The monitoring-edge-geodetic number meg⁡(G) is the cardinality of the minimum MEG-set in G. In this paper, we obtain the exact values or bounds for the MEG numbers of graph products, including join, corona, cluster, lexicographic products and direct products.