Locating-dominating number of certain infinite families of convex polytopes with applications.

A convex hull of finitely many points in the Euclidean space is known as a convex polytope. Graphically, they are planar graphs i.e. embeddable on . Minimum dominating sets possess diverse applications in computer science and engineering. Locating-dominating sets are a natural extension of dominating sets. Studying minimizing locating-dominating sets of convex polytopes reveal interesting distance-dominating related topological properties of these geometrical planar graphs. In this paper, exact value of the locating-dominating number is shown for one infinite family of convex polytopes. Moreover, tight upper bounds on are shown for two more infinite families. Tightness in the upper bounds is shown by employing an updated integer linear programming (ILP) model for the locating-dominating number of a fixed graph. Results are explained with help of some examples. The second part of the paper solves an open problem in Khan (2023) [28] which asks to find a domination-related parameter which delivers a correlation coefficient of with the total -electronic energy of lower benzenoid hydrocarbons. We show that the locating-dominating number delivers such a strong prediction potential. The paper is concluded with putting forward some open problems in this area.