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 2 〉 h of benzenoids of size h grows as h 2ν , with ν = 0.64115(5).
|Number of pages||11|
|Journal||Journal of Chemical Information and Computer Sciences|
|Publication status||Published - 1 May 2002|