Geodetic Coalition Graphs

In this paper, we introduce the concept of the geodetic coalition graph derived from a given graph [Formula: see text] and its geodetic coalition partition. The geodetic coalition graph captures the interactions between geodetic coalition partners. We investigate structural properties of geodetic coalition graphs and compute them for standard graph families including paths, cycles, complete graphs and trees. A real-world application is demonstrated by modeling delivery hub systems using geodetic coalition graphs, showcasing their potential in optimizing route coverage and connectivity. This study extends the utility of geodetic principles in coalition based graph modeling.