Cluj and Omega Polynomials in PAHs and Fullerenes

A graph property P(G), written as a sequence of numbers counting its local partitions, can be expressed as a counting polynomial P(G,x) with the exponents of the indeterminate x showing the extent of partitions p(G), υ p(G) = P(G) while the coefficients are related to the number of partitions occurrence. Definitions and properties of Cluj CJ(G, x) and Ω(G, x) polynomials and their relation with other topological descriptors are presented. Analytical relations for calculating these polynomials and corresponding topological indices in some classes of PAHs are derived. The ability of topological descriptors to predict various physico-chemical and biological properties is reviewed. Omega polynomial applied to small fullerenes provided a single number descriptor useful in predicting their energetic stability.