The Pi polynomial and the Pi index of a family hydrocarbons molecules

Mohammad Reza Farahani and M.

Abstract

Let G be a simple molecular graph without directed and multiple edges and without loops, the vertex and edge-sets of which are represented by V(G) and E(G), respectively. A topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. A new counting polynomial, called the Omega polynomial, was recently proposed by Diudea on the ground of quasi-orthogonal cut "qoc" edge strips in a polycyclic graph. Another new counting polynomial called the Pi polynomial. The Omega and Pi polynomials are equal to Ω(G,x)= (G, )xc cΣ m c and Π(G,x)= ( ) ( ) , .c.x E G c c m G c - Σ , respectively. In this paper, the Pi polynomial and the Pi Index of Polycyclic Aromatic Hydrocarbons PAHk are computed.