On certain counting polynomials and subsequent indices of certain chemical graphs

Abstract

Counting polynomials and the single number descriptors attained from them give rise to more curiosity in mathematical chemistry with the aid of graph theory. Over the last few decades, countless researchers have placed their effort into counting polynomials and providing results on molecular descriptors for distinctive families of molecular structures. Counting polynomials have an exponential value equal to the proportions of a characteristic partitioning and coefficients proportional to the number of different parts. From these polynomials, molecular invariants are described. It is possible to deduce several fundamental invariants from polynomials by either directly taking their value at a certain point or by calculating the derivatives or integrals of the polynomial. The concept of a counting polynomial was first established by Polya 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 indices by numerical methods. Certain firmly related polynomials, namely theta and omega, subordinate the equidistant edges. PI and Sadhana polynomials subordinate the nonequidistant edges of structural graphs, which have a rich application in various fields. newline