ISOMERS OF POLYCYCLIC CONJUGATED HYDROCARBONS WITH ARBITRARY RING SIZES - GENERATION AND ENUMERATION

Completely condensed polycyclic conjugated hydrocarbons are studied with respect to their numbers of C(n)H(s) isomers (# I) for arbitrary ring sizes. Direct combinatorial methods are applied and based on the ring-edge sum (SIGMAq), viz. the sum of all edges in the q-membered rings taken individually. Explicit expressions of # I are reported for two rings (r = 2) and three rings (r = 3). The latter case (r = 3) splits into structures without any internal carbon (n(i) = 0) and those with one internal carbon (n(i) = 1). Finally, the corresponding problem for r = 4, n(i) = 1 is solved by means of computer programming.