Abstract <p>Graph theory provides a solid mathematical foundation in several fields. It is helpful to describe complex systems by representing items as vertices and their relationships as edges. This study examines the structural properties of three nanostructures. Melem chains are polymeric carbon nitride structures. The stability and photocatalytic activity of covalent triazine bonds make them valuable for optoelectronic devices and solar energy conversion. Borophene chains are promising materials for energy storage and nanoelectronics. Boron triangular sheets are highly promising for quantum materials due to their remarkable mechanical strength and hexagonal structure. We calculate several reduced reverse topological indices, including the geometric–arithmetic, general Randić, and hyper-Zagreb indices. For large-scale nanostructures, calculating reduced reverse indices requires billions of edge-degree operations. Such operations require high-performance computing resources with parallel and distributed architectures to enable real-time assessment of descriptors. This supercomputing alignment provides scalability for drug discovery, optoelectronic simulations, and nanomaterial design. This study also includes a comprehensive graph-theoretical comparison to evaluate the importance of the results.</p> Graphical abstract <p></p>