KEKULE STRUCTURES AS GRAPH GENERATORS

Kekule valence-bond structures of catacondensed conjugated hydrocarbons with no, one, two and three branched cycles (which may be 4-, 6- and/or 8-membered) are used to generate highly regular vertex-transitive graphs through the application of an equivalence relation to the sextet of pi-electrons in the terminal rings of the hydrocarbon. The partitioning of a given set of Kekule structures allows the study of certain novel combinatorial aspects of Kekule counts. The graph-generating character reported here is closely related to the recent work of Randic, Woodworth, Kleiner and Hosoya.