Research Articles
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
Muhammad Idrees,
University of Education, Lahore, PK
About Muhammad
Division of Science and Technology
Numan Amin,
GC University, Lahore, PK
About Numan
Abdus Salam School of Mathematical Sciences
Zaffar Iqbal
University of Gujrat, PK
About Zaffar
Department of Mathematics
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
Downloads
