Hosoya polynomial and topological indices of n-linear benzene

Abstract

The Hosoya polynomial was introduced by Hosoya in 1988 for a molecular graph G as H (G, x) = ∑d(G) d (G,k) xk where d(G, k) is the number of pairs of vertices of G laying at k-1 distance k from each other to count the number of paths of different lengths in G. The most interesting application of the Hosoya polynomial is that almost all distance-based topological indices can be recovered from it. In this article, we give the general closed form of the Hosoya polynomial of n times linearly concatenated benzene molecule Bn by partitioning the vertices of Bn and by using induction to find sums of distances of different lengths in Bn. We also find Wiener, hyper Wiener, Harary, and TSZ indices to predict physical, chemical and pharmacological properties of Bn and molecules containing Bn.