Omega, Sadhana, and PI Polynomials of Quasi-Hexagonal Benzenoid Chain

Counting polynomials are important graph invariants whose coefficients and exponents are related to different properties of chemical graphs. Three closely related polynomials, i.e., Omega, Sadhana, and PI polynomials, dependent upon the equidistant edges and nonequidistant edges of graphs, are studied for quasi-hexagonal benzenoid chains. Analytical closed expressions for these polynomials are derived. Moreover, relation between Padmakar-Ivan (PI) index of quasi-hexagonal chain and that of corresponding linear chain is also established.