Enumeration of chemical isomers of polycyclic conjugated hydrocarbons with six-membered and five-membered rings

Polygonal systems P consist of exclusively hexagons and pentagons. They correspond (as chemical graphs) to a certain class of polycyclic conjugated hydrocarbons. This class includes protofullerenes. General formulations for the maximum numbers of internal vertices for P systems with p less than or equal to 6 are derived; here p is the number of pentagons. The CnHs chemical formulas of P systems are studied with special emphasis on the semibuckminsterfullerene (C30H12), circum-semibuckminsterfullerene (C58H16) and corannulene (C20H10) isomers. Numbers of all CnHs isomers for P systems with r less than or equal to 6 are computed; here r is the total number of polygons.