Groupe d’études et de recherche en analyse des décisions

# Recursive and Explicit Formulae for the Degree of Freedom of Cata-Condensed Benzenoid Hydrocarbons

## Pierre Hansen et Maolin Zheng

It is shown that the degree of freedom of a Kekulé structure K of a cata-condensed benzenoid hydrocarbon H is equal to the number of maximum disjoint hexagons containing three double bonds. From this property, a recursive relation for the degree of freedom of H is derived. By using the powerful generating function method, closed form formulae for the degree of freedom of three infinite classes of cata-condensed benzenoid hydrocarbons are obtained.

, 18 pages