The Sadhana polynomial and the Sadhana index of polycyclic aromatic hydrocarbons PAHK

Shaohui Wang, Mohammad Reza Fa

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. 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)= (G, )xc cΣ m c with m(G,c) being the number of strips of length c. Also, know that the Sadhana polynomial and the Sadhana Index are equal to Sd(G,x)= ( ) ( , )xE G c cΣ m G c - and Sd(G)= ( , )( ( ) ) cΣ m G c E G -c , respectively. The aim of this paper is to compute this counting polynomial and its index of an family of hydrocarbons that we named: Polycyclic Aromatic Hydrocarbons PAHk ("k≥1).