On the strong geodeticity in the corona type product of graphs

TL;DR

This paper investigates the properties of strong geodetic sets in various corona-type product graphs, providing formulas and insights into how these structures influence geodetic coverage.

Contribution

It introduces new formulas for strong geodetic numbers in generalized corona products based on the properties of the initial graphs.

Findings

Derived formulas for strong geodetic numbers in corona-type products.

Analyzed how structural properties affect geodetic coverage.

Expanded understanding of geodetic parameters in product 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.