ISSN print edition: 0366-6352 ISSN electronic edition: 1336-9075 Registr. No.: MK SR 9/7 Published monthly

Exploring statistical relationships between Revan topological indices and Gibbs energy in titanium diboride

Rimsha Saher, Ziyattin Tas, Atef F. Hashem, Muhammad Kamran Siddiqui, and Muhammad Farhan Hanif

Department of Mathematics, COMSATS University Islamabad, Lahore, Pakistan

E-mail: rimshasaher382@gmail.com

Received: 3 October 2025  Accepted: 29 November 2025

Abstract:

In this paper we are discussing state relations between some Revan topological indices and the Gibbs free energy of the molecular network of Titanium Diboride. The structural influence on thermodynamic properties is addressed by considering Titanium Diboride as a molecular graph, and calculating a few Revans and Hyper Revan indices. We presented a full computational pipeline, which included graph construction, vertex and edge partition, calculation of the analytical index and verification in Python, as well as visualization for MATLAB. Polynomial curve fitting was applied for the modelling of how individual topological indices change in relation with changes in Gibbs free energy for various structural conformations. Model validation was done using standard statistical indices, which all indicated a remarkable fit of predicted to observed values. These results suggest that the Revan indices are effective in describing the structure and thermodynamics of inorganic materials. The work underlines the applicability of topological descriptors as inexpensive computational methodologies to describe compounds which may complement more costly experimental measurements. This work is part of the trend towards an increasing role of computational chemistry and promotes graph-theoretic approaches to predicting material stability and for the design of advanced ceramic and inorganic systems.

Keywords: Revan topological indices; Gibbs free energy; Titanium diboride; Molecular graph; Statistical correlation; Thermodynamic stability; Computational chemistry; Materials science.

Full paper is available at www.springerlink.com.

DOI: 10.1007/s11696-025-04573-9

Chemical Papers 80 (3) 3095–3112 (2026)