A mathematical investigation for appraisal of crystal structure lattices through eccentricity-based topological invariants, QSPR analysis, and MCDA

Chemical graph theory has become the eye of chemists to manipulate each compound for its multipartite physiochemical properties when investigated through topological invariants. Our targeted structures are symmetrically highly delicate crystal lattice structures, namely face-centered cubic (FCC( N )), hexagonal-close packed (HCP( N )), and hexagonal (HEX( N )) crystal structures, where N defines finite number of unit cells. The topological invariants having great predicting and correlating properties, namely eccentric connectivity, connective eccentric, total eccentricity, and eccentricity-based Zagreb, have been investigated for these crystal lattice structures. The effective and expanding application of chemical graph theory, named QSPR (quantitative structure–property relationship), has been implemented in this research work to predict five physiochemical properties, namely melting point, boiling point, density, molar heat capacity, and enthalpy. Undoubtedly, it is not a big deal to see which structure is more efficient and dominating or not when visualized through the numerical values obtained from each topological invariant. This research work is directed toward the study of when we have finite graph structures studied via various topological invariants and the outcomes and predictions obtained from QSPR analysis; then, how we can reach the one best structure keeping in view each of its properties and the effects of conclusions obtained from statistical reasoning. This led us to introduce another highly operational field of mathematics named OR (operations research) that ranks multiple objects when they are constrained through multiple criteria. In this work, the objects we have considered are the graph structures and the criteria are the predicted values obtained from QSPR statistical reasoning. For reaching the best-defined crystal structure lattice, we have used the highly effective technique of MCDA (multiple criteria decision analysis) named as VIKOR. This technique is exceedingly constructed with the background and the effects of conclusions generated by multiple regression analysis in QSPR modeling.