On Bounds for Strong Metric Dimension of Two Families of Convex Polytopes

Abstract

The strong metric dimension is a graph invariant that strengthens the classical notion of metric dimension by requiring that every pair of vertices be strongly resolved by at least one vertex lying on a shortest path between them. This parameter has attracted considerable attention due to its theoretical significance and applications in network analysis. Convex polytopes constitute an important class of highly symmetric planar graphs, yet their strong metric dimension has not been extensively studied. In this paper, we investigate the strong metric dimension of two families of convex polytopes. By analyzing their structural properties and distance relations, we determine bounds for the strong metric dimension for each family. Our results enrich the existing literature on metric-based graph invariants of polytope graphs and provide further insight into the interplay between geometric structure and strong resolvability.