Computing a Counting Polynomial of an Infinite Family of Linear Polycene Parallelogram Benzenoid Graph P(a,b)

Omega polynomial was defined by M.V. Diudea in 2006 as  where the number of edges co-distant with e is denoted by n(e). One can obtain Theta Θ, Sadhana Sd and Pi Π polynomials by replacing xn(e) with n(e)xn(e), x|E|-n(e) and n(e)x|E|-n(e) in Omega polynomial, respectively. Then Theta Θ, Sadhana Sd and Pi Π indices will be the first derivative of Θ(x), Sd(x) and Π(x) evaluated at x=1. In this paper, Pi Π(G,x) polynomial and Pi Π(G) index of an infinite family of linear polycene parallelogram benzenoid graph P(a,b) are computed for the first time