Sadhana and PI polynomials and their indices of an infinite class of the titania nanotubes TiO2(m, n)

Let G = (V, E) be a simple connected molecular graph in chemical graph theory, where the vertex set and edge set of G denoted by V (G) and E(G) respectively. Two edges e = uv and f = xy of G are called co-distant (briefly: ecof ) if they obey the topologically parallel edges relation. The Sadhana polynomial of a graph G Sd(G,x) for counting qoc strips in G was defined by Ashrafi et al. as Sd(G,x) =σc m(G,c)xE(G)-c and the Sadhana index of G is Sd(G) =σc m(G,c)(E)G-c), where m(G,c) being the number of qoc strips of length c. In this paper, we compute the Sadhana Sd(G,x) and Pi II G(x)=σc m(G,c) · c ·xE(G)c.