Mohammad Reza Farahani, Π(G,x) Polynomial and Π(G) Index of Armchair Polyhex Nanotubes TUAC6[m,n], ILCPA Volume 36, International Letters of Chemistry, Physics and Astronomy (Volume 36)
https://www.scipress.com/ILCPA.36.201
Abstract:
    Let <i>G</i> be a simple connected graph with the vertex set <i>V = V(G)</i> and the edge set <i>E = E(G)</i>, without loops and multiple edges. For counting <i>qoc</i> strips in <i>G</i>, Omega <i>polynomial</i> was introduced by <i>Diudea</i> and was defined as Ω(G,x) = ∑<sub>c</sub>m(G,c)x<sup>c</sup> where m(G,c) be number of <i>qoc</i> strips of length <i>c</i> in the graph <i>G</i>. Following Omega polynomial, the Sadhana polynomial was defined by <i>Ashrafi</i> et al as Sd(G,x) = ∑<sub>c</sub>m(G,c)x<sup>[E(G)]-c</sup> in this paper we compute the <i>Pi</i> polynomial Π(G,x) = ∑<sub>c</sub>m(G,c)x<sup>[E(G)]-c</sup> and <i>Pi</i> Index Π(G ) = ∑<sub>c</sub>c·m(G,c)([E(G)]-c) of an infinite class of “<i>Armchair polyhex nanotubes TUAC<sub>6</sub>[m,n]</i>”<i>.</i>
Keywords:
    Armchair Polyhex Nanotubes, Molecular Graph, Nanotori, Omega Polynomial, Pi Index, Pi Polynomial