Sharp bounds of partition resolvability of convex polytopes

Graph theory serves as a central and dynamic framework for the design and analysis of networks. Convex polytopes, as fundamental geometric entities, encompass a rich variety of mathematical structures and problems. The basic theory of convex polytopes involves the study of faces, normal cones, duality—particularly polarity—along with separation and other elementary concepts. A convex polytope can be described as a convex set of points within the \ (n\) -dimensional Euclidean space \ (^n\). Among the various dimensions, the partition dimension is the most challenging, and determining its exact value is an NP-hard problem. In this work, we establish bounds for the partition dimension of convex polytopes \ (T_\), \ (R_\), and \ (U_\).