@article {
author = {Xu, S.-J. and He, Q.-H. and Zhou, S. and Chan, W.},
title = {Hosoya Polynomials of Random Benzenoid Chains},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {7},
number = {1},
pages = {29-38},
year = {2016},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2016.11867},
abstract = {Let $G$ be a molecular graph with vertex set $V(G)$, $d_G(u, v)$ the topological distance between vertices $u$ and $v$ in $G$. The Hosoya polynomial $H(G, x)$ of $G$ is a polynomial $sumlimits_{{u, v}subseteq V(G)}x^{d_G(u, v)}$ in variable $x$. In this paper, we obtain an explicit analytical expression for the expected value of the Hosoya polynomial of a random benzenoid chain with $n$ hexagons. Furthermore, as corollaries, the expected values of the well-known topological indices: Wiener index, hyper-Wiener index and Tratch-Stankevitch-Zefirov index of a random benzenoid chain with $n$ hexagons can be obtained by simple mathematical calculations, which generates the results given by I. Gutman et al. [Wiener numbers of random benzenoid chains, Chem. Phys. Lett. 173 (1990) 403-408].},
keywords = {Wiener index,Random benzenoid chain,Hosoya polynomial,Expected value,Generating function},
url = {https://ijmc.kashanu.ac.ir/article_11867.html},
eprint = {https://ijmc.kashanu.ac.ir/article_11867_e0847f53fd013808c54145717912481c.pdf}
}