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

Entropy structure correlation and Nirmala topological analysis of single-layer polymeric tetraoxa circulene derivatives

Mazhar Hussain, Atef F. Hashem, Muhammad Farhan Hanif, A. K. Alzahrani, and Muhammad Aamer Rashid

Department of Mathematics and Statistics, The University of Lahore, Lahore Campus, Lahore, Pakistan

E-mail: mazhar6462@gmail.com

Received: 5 November 2025  Accepted: 4 December 2025

Abstract:

Abstract

Degree-based Nirmala indices were used to study the molecular topology versus information theoretic complexity of two single-layer polymeric tetraoxa circulene derivatives. Applying the graph-theoretical edge partitioning we obtained general formulas for original and inverted Nirmala indices, which measure, respectively, molecular connectivity and structural deviation. Graph based entropy measures were used to quantify complexity and statistically correlated with derived indices by means of a logarithmic regression. The reliable relationship between entropy and index was established with excellent R-squared values and low SE of the models. The results show that not only Nirmala descriptors act as quantitative structure property relationship, but also they are predictors of the molecular entropy. These results indicate that the Nirmala based descriptors are promising in serving as an indicator for structural characterization, molecular design, and quantitative modeling in materials chemistry and nanostructure study.

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Keywords: Tetraoxa circulene; Nirmala index; Topological indices; Logarithmic regression; Entropy modeling; 05C10; 05C09; 37B40

Full paper is available at www.springerlink.com.

DOI: 10.1007/s11696-025-04579-3

Chemical Papers 80 (3) 3189–3206 (2026)