On metric dimension of generalized subdivision prism graph

A convex polytope is a type of polytope that is defined as a convex set in n-dimensional Euclidean space. A graph is a mathematical structure formed up of a collection of interconnections between items called edges and a set of objects called vertices. In general, a graph is represented as an ordered pair $G=(V,E)$, where V stands for the set of vertices and E for the set of edges which are defined as unordered pairings of vertices. If for each pair of different vertices $x,y\in V$, there exists a vertex $w\in S$ such that the distance from w to x is not equal to the distance from w to y, then a set $S\subseteq V$ is a resolving set. The minimum cardinality of the resolving set is known as the metric dimension of a graph G. The computation of metric dimension for any graph is an essential concept with applications in mathematics, computer science, geometry, chemical science, etc. Metric dimension involves the smallest set of points needed to uniquely identify all other points in a network. In this research article, we take a family of a convex polytope, viz. generalized subdivision prism graph $J\left(F_n\right)$ and investigate its metric basis and metric dimension.