ISSN print edition: 0366-6352
ISSN electronic edition: 1336-9075
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From graph invariants to material insights: analytic investigation of MOF lattices

Guilin Tang, Sahar Aftab, Adnan Aslam, and Sadia Noureen

School of Computer and Network, Anhui Posts and Telecommunications College, Hefei, China

Received: 3 September 2025 Accepted: 27 October 2025

Abstract:

Metal–organic frameworks (MOFs) are a rapidly expanding class of materials valued for their high porosity, structural diversity, and potential in gas storage, separation, and catalysis. Understanding their connectivity through mathematical descriptors is essential for predicting structure–property relationships. Topological indices, which capture molecular architecture independently of geometry, offer a powerful framework for this purpose. In this study, we derive closed-form expressions for eight degree-based indices: atom bond connectivity (ABC), atom–bond sum connectivity (ABS), modified misbalance rodeg index (MMR), symmetric division indeg index (SDD), sigma index (SI), inverse sum indeg index (ISI), inverse symmetric division deg index (ISDD), and sum–connectivity index (SC), on three MOF-related lattice structures (Square Octagon Lattice, Hexagonal Carbophene framework and Rectangular Carbophene framework). These results, obtained via systematic edge partitions, provide scalable tools for analyzing large frameworks. To explore chemical significance, the indices are applied to 23 MOF linkers, with regression models developed to estimate boiling point, melting point, and molar refractivity. The analysis shows strong predictive performance, with SDD and ISDD emerging as the most reliable descriptors. This integration of graph theory and chemical informatics offers a cost-effective pathway for rational MOF design.

Keywords: Mathematical chemistry; Degree-based descriptors; Metal–organic frameworks (MOFs); Structure–property relationship; Regression models; 05C07; 05C90; 05C92; 92E10

Full paper is available at www.springerlink.com.

DOI: 10.1007/s11696-025-04500-y

Chemical Papers 80 (2) 1947–1964 (2026)

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