Applications of the Reduced Graph Model. Enumeration of Kekule Structures for Certain Classes of Large Benzenoid Hydrocarbons

The reduced graph model is applied to the enumeration of Kekule structures for several classes of large benzenoid hydrocarbons

Application of the Dualist Model. Generation of Kekule Structures and Resonant Sextets of Benzenoid Hydrocarbons

The dualist model of Balaban is used for the enumeiration and dis.play of Kelmle struotmres K aind .resooant sextet numbers rCG; k) O·f la.rge cata-condenrsed bemmnoi:d hydrncarbons. The key steps are: (1) Transfo.rm the berw;enoid graph into the corresponding dualist and associate with it a linear-angular, L-A, sequence, (2) Fragment the dualist into subgraphs after each L-A pair. The resulting subgraphs are called fragment graiphs. (3) Colour each fragment graph, containing v veritices, v + 1 times such ·that each co1ourin.g contaiins a.t mo&t on black vertex (the rest being white). ( 4) Re-assemble the coloured fragments into theiir initial geometry, preserved in the dual\u27ist, to produce a set o.f c10l0>ured dua!ists such that no coloured dualist has more than one black vertex in each linear segment. The number of such coloured duali:sts is K, the Kek•ule count. By convention, each blac.k dualist vertex corresponds to a propex resona,nt sextet. This, plus the fac.t that a lineair segment can have at most one resonant sexteit, completely defines all o.f the individual VB Kekule structures and their resonant sextets. The method is an illustration o.f data reduction schemes and is quite suited for large benzenoid hydrocarbons. A numbe•r O<f fo:rlIIlllllae for com,putiing the number of Kekule striuctures of vairious families of cata-condensed benzenoid hydrocarbons are derived. In addition, the abnve apprnach is applicable to large benzenoid systems consisting 0if c.ata- condensed f.ra,gments and thin peri-condensed fragments