#### Research Articles

# Hosoya polynomial and topological indices of n-linear benzene

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**Authors:**

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Abdul Rauf Nizami ,

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Faculty of Information Technology, University of Central Punjab, Lahore, Pakistan, PK

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Muhammad Idrees,

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Division of Science and Technology, University of Education, Lahore, Pakistan, PK

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Numan Amin,

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Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan, PK

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Zaﬀar Iqbal

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Department of Mathematics, University of Gujrat, Pakistan, PK

## Abstract

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}.

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How to Cite:
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Nizami, A.R., Idrees, M., Amin, N. and Iqbal, Z., 2019. Hosoya polynomial and topological indices of n-linear benzene. *Journal of the National Science Foundation of Sri Lanka*, 47(2).

Published on
21 May 2019.

Peer Reviewed

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