Structural identifiability in crystalline molecular networks using strong metric dimension.

Structural identifiability in crystalline molecular systems can be examined using graph-theoretic distance measures that capture the uniqueness of vertex positions within molecular networks. In this study, we investigate the strong metric dimension (SMD) of two crystalline frameworks, the Benzenoid Tripod and Bismuth Tri-Iodide chain, as representative models for aromatic and inorganic lattices. A vertex strongly identifies a pair of vertices if it lies on a shortest path between them, and the minimal set of such vertices defines the SMD of the network. By employing the Oellermann-Fransen approach, the strong resolving graphs of both crystalline networks are constructed, and the vertex-cover method is applied to obtain exact SMD values. Analytical derivations reveal structural patterns linking the topology of benzenoid rings and bismuth-iodide layers to their identification capacities. The results indicate that the SMD serves as a quantifier of information completeness within crystalline graphs, analogous to connectivity measures used in cheminformatics and network science. A conjecture is further proposed for the two-dimensional bismuth tri-iodide sheet, offering a pathway toward generalized formulations for layered crystalline materials. The proposed framework bridges discrete mathematics and molecular modeling, demonstrating how strong metric identification can support structural verification, nano-design, and data-driven exploration of chemical networks.