## Abstract

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).

Original language | English |
---|---|

Pages (from-to) | 456-466 |

Number of pages | 11 |

Journal | Journal of Chemical Information and Computer Sciences |

Volume | 42 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 May 2002 |

Externally published | Yes |