M-Polynomials and degree-based topological indices of the two dimensional Coronene fractal structures

Muhammad Asif  Javed; A. Q. Baig; Mukhtar Ahmad; Roslan Hasni; Kai Siong Yow; Ather Qayyum

doi:10.5269/bspm.77074

Muhammad Asif Javed Department of Mathematics, University of Southern Punjab Multan, Pakistan
A. Q. Baig Department of Mathematics, Statistics University Of Southern Punjab, Multan
Mukhtar Ahmad Department of Mathematics, Khawaja Fareed University of Engineering and Information Technology Rahim Yar Khan, Pakistan
Roslan Hasni Special Interest Group on Modeling and Data Analytics (SIGMDA) Faculty of Computer Science and Mathematics Universiti Malaysia Terengganu 21030 Kuala Nerus, Terengganu, Malaysia
Kai Siong Yow Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Malaysia
Ather Qayyum Department of Mathematics, Statistics University Of Southern Punjab, Multan

Resumen

Topological indices are numerical descriptors widely used to investigate the structural, physical, and chemical properties of molecular compounds. Among them, degree-based topological indices have demonstrated strong correlations with a variety of molecular characteristics, making them a central topic in chemical graph theory. The M-polynomial serves as a powerful generating function for deriving such indices. In this study, we present closed-form expressions for several important degree-based topological indices associated with the zigzag molecular graph of two-dimensional coronene fractal structures. The indices examined include the first and second Zagreb indices, the modified Zagreb index, the symmetric division index, the harmonic index, the Randi´c index, the inverse Randic index, and the augmented Zagreb index. The derivations are carried out using a calculus-based approach, offering deeper insights into the topological and structural features of these nanostructures.

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