Hosoya polynomials of random benzenoid chains

Shou-Jun XU, Qing-Hua HE, Shan ZHOU, Wai Hong CHAN

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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.
Original languageEnglish
Pages (from-to)29-38
JournalIranian Journal of Mathematical Chemistry
Issue number1
Publication statusPublished - Mar 2016


Xu, S.-J., He, Q.-H., Zhou, S., & Chan, W. H. (2016). Hosoya polynomials of random benzenoid chains. Iranian Journal of Mathematical Chemistry, 7(1), 29-38.


  • Wiener index
  • Random benzenoid chain
  • Hosoya polynomial
  • Expected value
  • Generating function


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