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Hosoya polynomial and topological indices of n-linear benzene

Authors:

Abdul Rauf Nizami ,

University of Central Punjab, Lahore, PK
About Abdul Rauf
Faculty of Information Technology
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Muhammad Idrees,

University of Education, Lahore, PK
About Muhammad
Division of Science and Technology
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Numan Amin,

GC University, Lahore, PK
About Numan
Abdus Salam School of Mathematical Sciences
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Zaffar Iqbal

University of Gujrat, PK
About Zaffar
Department of Mathematics
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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

How to Cite: 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), pp.169–174. DOI: http://doi.org/10.4038/jnsfsr.v47i2.9152
Published on 25 Jul 2019.
Peer Reviewed

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