On counting polynomials of certain classes of polycyclic aromatic hydrocarbons

Abstract

Polya was the first to establish the concept of a counting polynomial in chemistry. Despite the fact that the spectra of the characteristic polynomial of graphs were exhaustively researched by quantitative means in order to ascertain the molecular orbitals of unsaturated hydrocarbons, the field garnered little attention from chemists for several decades. Polynomials can be used to produce a variety of significant topological indices, either explicitly or after calculating derivatives or numerical methods. Certain firmly related polynomials, namely Theta, Omega, PI, and Sadhana polynomials, subordinate the equidistant edges and non-equidistant edges of structural graphs, which have a rich application in computing the corresponding topological indices. A topological index is a numerical value associated with a network that predicts chemical, physical, and biological activities. This article investigates these polynomials for three classes of polycyclic aromatic hydrocarbons as hexa-peri-hexabenzocoronene, hexa-cata-hexabenzocoronene, and dodeca-benzo-circumcoronene. In addition, closed formulas for these polynomials’ corresponding indices are proposed.