Hosoya polynomials of random phenylene chains

摘要

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 Sigma({u,v}subset of 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 phenylene 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 Phenylene chain with n hexagons can be obtained by simple mathematical calculations.