Computing Θ(G,x) and Π(G,x) Polynomials of an Infinite Family of Benzenoid

The topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. The Omega polynomial Ω(G,x) for counting qoc strips in G is defined as Ω(G,x) = Σc m(G,c)xc with m(G,c) being the number of strips of length c. Other three related polynomials can be calculated on ops as Θ(G,x) = Σcm(G,c)cxc, Sd(G,x) = Σcm(G,c)x|E(G,x)|-c and Π(G,x) = Σcm(G,c)cx|E(G)|-c. The above polynomials count codistant and non-codistant edges, respectively. In this paper we compute the Theta Θ(G,x), Pi Π(G,x) polynomials and the corresponding indices in the circumcoronene series of benzenoids.