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

Multiplicative neighborhood degree based indices of carbon nanostructures

Sadia Kausar, Quanita Kiran, Yasir Ali, and Muhammad Imran

College of Electrical and Mechanical Engineering, National University of Sciences and Technology, Rawalpindi, Pakistan

E-mail: sadiausman44404@gmail.com

Received: 15 October 2025  Accepted: 24 January 2026

Abstract:

Topological indices have long been used in QSPR (Quantitative Structure–Property Relationship) studies as they summarize molecule’s structure to predict its physicochemical properties. In this work, we derive closed formulas for the novel multiplicative neighbourhood mev-degree and mve-degree based topological indices for some carbon nanostructures, namely, generalized nanotube, generalized nanocone, H-naphthalenic nanosheet and two dimensional structure of graphene. These structures provide foundational models for many carbon nanomaterials and are crucial for designing advanced field emitters, catalytic supports, energy storage in batteries and super capacitors etc. Nanomaterials in general exhibit complex bonding patterns in which atoms at corners and interior positions contribute differently to the overall topology mev and mve-degree based topological indices effectively capture these structural variations by incorporating vertex–edge interaction information. Consequently, these indices provide a reliable framework for the mathematical characterization of complex nanomaterial structures.

We present this fact through the computation of numerical values of some famous indices and their graphical illustrations, to gauge their consistent trends with the growing nanostructures. Due to limited experimental exploration, the data for many of the physicochemical properties of nanostructures is still not available. However, our results provide a baseline estimate in predicting various properties of carbon nanostructures like \(\pi -\)electron energy, boiling point, retention volume and strain energy etc.

Keywords: Molecular topological index; Nanostructre; Graphene; QSPR

Full paper is available at www.springerlink.com.

DOI: 10.1007/s11696-026-04700-0

Chemical Papers 80 (4) 4391–4407 (2026)