On the Number of Benzenoid Hydrocarbons

Markus Vöge, Anthony J. Guttmann, Iwan Jensen

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)


We present a new algorithm which allows a radical increase in the computer enumeration of benzenoids b h with h hexagons. We obtain b h up to h = 35. We prove that b h ∼ const.κ h , prove the rigorous bounds 4.789 ≤ κ ≤ 5.905, and estimate that κ = 5.16193016(8). Finally, we provide strong numerical evidence that the generating function ∑b h Z h ∼ A(Z) log(1 - κZ), estimate A(1/κ) and predict the subleading asymptotic behavior. We also provide compelling arguments that the mean-square radius of gyration 〈R g 2h of benzenoids of size h grows as h , with ν = 0.64115(5).

Original languageEnglish
Pages (from-to)456-466
Number of pages11
JournalJournal of Chemical Information and Computer Sciences
Issue number3
Publication statusPublished - 1 May 2002
Externally publishedYes


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