Abstract
Let G be a graph with vertex set and edge set . For any and , the edge e is monitored by two vertices u and v in graph G if . A set M of vertices of G is a monitoring-edge-geodetic set of G if for any edge there exists a pair such that e is monitored by u, v. The monitoring-edge-geodetic number 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.
Acknowledgments
The author thanks the anonymous referee for many helpful comments and correcting errors in the paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).