Abstract
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 d G ( u , v ) ≠ d G − 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.
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