Metric dimension of structured networks with symmetry: Algorithms and applications

This study examines the metric dimension (MD) invariance in modified convex polytope structures, focusing on changes like adding [Formula: see text] times pendant edges and adding [Formula: see text] times prisms to the outer cycle of some convex polytope structures. MD, a key graph theory concept, has applications in network design, molecular analysis, and fault-tolerant systems. The research aims to examine that these modified polytopes have a constant MD, assess their computational complexity, and explore their applications in resilient system design. Results indicate that MD remains invariant, which aids in efficient vertex identification and supports applications in traffic management, power grids, and sensor network optimization. Overall, the study connects theoretical insights with practical uses, emphasizing the importance of invariant metric properties in advancing graph theory and its real-world applications.