Hosoya polynomials of random benzenoid chains

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].