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**1 - 2**of**2**### A Constructive Enumeration of Fusenes and Benzenoids

"... In this paper, a fast and complete method to constructively enumerate fusenes and benzenoids is given. It is fast enough to construct several million non isomorphic structures per second. The central idea is to represent fusenes as labelled inner duals and generate them in a two step approach using ..."

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In this paper, a fast and complete method to constructively enumerate fusenes and benzenoids is given. It is fast enough to construct several million non isomorphic structures per second. The central idea is to represent fusenes as labelled inner duals and generate them in a two step approach using the canonical construction path method and the homomorphism principle.

### ARTICLES On the Number of Benzenoid Hydrocarbons

, 2001

"... We present a new algorithm which allows a radical increase in the computer enumeration of benzenoids bh with h hexagons. We obtain bh up to h) 35. We prove that bh const.h, prove the rigorous bounds 4.789 e e 5.905, and estimate that ) 5.16193016(8). Finally, we provide strong numerical evidence ..."

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We present a new algorithm which allows a radical increase in the computer enumeration of benzenoids bh with h hexagons. We obtain bh up to h) 35. We prove that bh const.h, prove the rigorous bounds 4.789 e e 5.905, and estimate that ) 5.16193016(8). Finally, we provide strong numerical evidence that the generating function ∑bhzh A(z) log(1- z), estimate A(1/) and predict the subleading asymptotic behavior. We also provide compelling arguments that the mean-square radius of gyration 〈Rg2〉h of benzenoids of size h grows as h2î, with î) 0.64115(5). 1.