A parallel algorithm for the enumeration of benzenoid hydrocarbons

Abstract

We present an improved parallel algorithm for the enumeration of fixed benzenoids B_h containing h hexagonal cells. We can thus extend the enumeration of B_h from the previous best h=35 up to h=50. Analysis of the associated generating function confirms to a very high degree of certainty that $B_h\sim A{\kappa }^h/h$ and we estimate that the growth constant $\kappa =5.161930154(8)$ and the amplitude $A=0.2808499(1)$.

14 pages, 6 figures