Vertex-based resolvability parameters for some families of convex polytopes.

In a k -dimensional space, convex polytopes are defined as the structures characterized by having straight line segments as edges, planar surfaces as faces and ensuring that line segment connecting any two points within the polytopes remains stay within the polytope. Their convex nature, with simplicity and intricate mathematical properties make them intriguing and pose significant challenges across various branches of mathematics and applications. Let G = (V , E) be a simple, connected and undirected graph of order  g. If vectors of distances of distinct vertices of G with respect to the set A are distinct, then the set A is called a resolving set or vertex resolving set for G. A resolving set for G with least possible cardinality is termed as metric basis for G and the number of elements in a metric basis for G is known as the metric dimension of the graph G. In this paper, we prove that the metric dimension is three for two closely related families of convex polytopes. [ABSTRACT FROM AUTHOR]