Mathematical techniques for graph descriptors, entropies, spectra, and properties of oxalate-based metal organic frameworks

Metal organic frameworks (MOFs) are not only fundamentally interesting due to their intricate and complex network structures but also due to their applied significance in enhancing the performance of various technologies, owing to their porous nature, large surface areas, and tunable structural architecture. Hence, they find applications in energy storage, catalysis, gas separation, and sensing technologies. Oxalates play a key role in the sequestration of toxic metal ions through efficient MOFs with tunable pores. This paper investigates graph descriptors, entropy, and spectral properties of oxalate-based MOFs. We have developed innovative mathematical methods to calculate distance based graph descriptors for a series of interconnected pentagonal networks that represent MOFs. We also compute the spectral based graph energies and the entropies of MOFs using techniques of graph theory. We have presented a regression technique for the efficient generation of the graph energies of these networks from their graph descriptors.