Hosoya polynomial and topological indices of n-linear benzene

The ？Hosoya ？polynomial ？was ？introduced ？by ？Hosoya ？in ？1988 ？for ？a ？molecular ？graph ？G ？as H (G, x) = ∑^d(G) ？d (G,k) x^{k？ ？？}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 B_n by partitioning the vertices of B_n and by using induction to find sums of distances of different lengths in B_n. We also find Wiener, hyper Wiener, Harary, and TSZ indices to predict physical, chemical and pharmacological properties of B_n and molecules containing B_n.？