On the strong geodeticity in the corona type product of graphs

Abstract: The paper focuses on studying strong geodetic sets and numbers in the context of corona-type products of graphs. Our primary focus is on three variations of the corona products: the generalized corona, generalized edge corona, and generalized neighborhood corona products. A strong geodetic set is a minimal subset of vertices that covers all vertices in the graph through unique geodesics connecting pairs from this subset. We obtain the strong geodetic set and number of the corona-type product graph using the strong 2-geodetic set and strong 2-geodetic number of the initial arbitrary graphs. We analyze how the structural properties of these corona products affect the strong geodetic number, providing new insights into geodetic coverage and the relationships between graph compositions. This work contributes to expanding research on the geodetic parameters of product graphs.