Let G be a simple connected graph with the vertex set V = V(G) and the edge set E = E(G), without loops and multiple edges. For counting qoc strips in G, Omega polynomial was introduced by Diudea and was defined as Ω(G,x) = ∑cm(G,c)xc where m(G,c) be number of qoc strips of length c in the graph G. Following Omega polynomial, the Sadhana polynomial was defined by Ashrafi et al as Sd(G,x) = ∑cm(G,c)x[E(G)]-c in this paper we compute the Pi polynomial Π(G,x) = ∑cm(G,c)x[E(G)]-c and Pi Index Π(G ) = ∑cc·m(G,c)([E(G)]-c) of an infinite class of “Armchair polyhex nanotubes TUAC6[m,n]”.
International Letters of Chemistry, Physics and Astronomy (Volume 36)
M. R. Farahani "Π(G,x) Polynomial and Π(G) Index of Armchair Polyhex Nanotubes TUAC6[m,n]", International Letters of Chemistry, Physics and Astronomy, Vol. 36, pp. 201-206, 2014