Hosoya polynomials of random benzenoid chains

Let G be a molecular graph with vertex set V(G), dɢ(u, v) the topological distance between vertices u and v in G. The Hosoya polynomial H(G, x) of G is a polynomial ∑{u, v} subseteq  V(G)ᵡᵈᴳ⁽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]. Copyright © 2016 University of Kashan Press.