Hosoya polynomials of random benzenoid chains

Abstract

Let G be a molecular graph with vertex set V(G) and dG(u,v) be the topological distance between vertices u and v in G. The Hosoya polynomial H(G,x) of G is a polynomial d x 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).