TY - JOUR
ID - 11867
TI - Hosoya Polynomials of Random Benzenoid Chains
JO - Iranian Journal of Mathematical Chemistry
JA - IJMC
LA - en
SN - 2228-6489
AU - Xu, S.-J.
AU - He, Q.-H.
AU - Zhou, S.
AU - Chan, W. H.
AD - Lanzhou University
AD - Jiangsu Normal University
AD - waihchan@ied.edu.hk
Y1 - 2016
PY - 2016
VL - 7
IS - 1
SP - 29
EP - 38
KW - Wiener index
KW - Random benzenoid chain
KW - Hosoya polynomial
KW - Expected value
KW - Generating function
DO - 10.22052/ijmc.2016.11867
N2 - 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].
UR - https://ijmc.kashanu.ac.ir/article_11867.html
L1 - https://ijmc.kashanu.ac.ir/article_11867_e0847f53fd013808c54145717912481c.pdf
ER -