On some counting polynomials and energy properties of superphenalene and supertriphenylene

In order to generate a wide range of meaningful topological indices, counting polynomials can be utilised in a number of different ways, including explicitly, after calculating derivatives. Certain polynomials, particularly Theta, Omega, Padmakar-Ivan, and Sadhana polynomials, are subservient to the equidistant and non-equidistant edges of graphs. Such polynomials have a wide range of applications, including the computation of the topological indices that correspond to them. Counting polynomials and corresponding indices in the context of super-polycyclic aromatic compounds with hexabenzocoronene as a base molecule, including superphenalene and supertriphenylene, refer to mathematical representations that encode structural information about the molecules. In addition, we have been able to acquire the spectral and energetic characteristics of these structures, which include the HOMO-LUMO gaps, bond delocalisation energies, and 13C NMR patterns.