Computation of Omega, Sadhana, and PI Polynomials for Molecular Descriptors in Two-Dimensional Coronene-Based Fractal Structures

Muhammad Asif Javed Javeed; A. Q. Baig; Mukhtar Ahmad Ahmad

doi:10.5269/bspm.77385

Muhammad Asif Javed Javeed Department of Mathematics, University of Southern Punjab Multan, Pakistan
A. Q. Baig Department of Mathematics and Statistics, University Of Southern Punjab, Multan, Pakistan
Mukhtar Ahmad Ahmad Department of Mathematics, Khawaja Fareed University of Engineering and Information Technology Rahim Yar Khan, Pakistan

Resumo

Counting polynomials serve as powerful tools in chemical graph theory, where exponents represent property-based partitions and coefficients denote their multiplicities. Originating from the study of quasi-orthogonal edge cuts in polycyclic graphs, these polynomials play a significant role in the topological characterization of bipartite structures and in deriving single-value molecular descriptors, such as topological indices. Specifically, they facilitate the enumeration of equidistant and non-equidistant edges within molecular graphs. In this study, we analytically compute the Omega, Sadhana, and PI counting polynomials for benzenoid nanotubes derived from two-dimensional coronene-based fractal structures. Closed-form expressions of these polynomials are derived for various molecular frameworks, including the circumcoronene series of benzenoids $H_\ell$ , hexagonal sheets, and zigzag-edge non-Kekulé benzenoids denoted by
$\Bbbk (p, q, r)$). The results contribute to the structural analysis and descriptor formulation of complex nanostructured materials.

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