Abstract
Kekulé 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 π-electrons in theterminal rings of the hydrocarbon. The partitioning of a given set of Kekulé structures allows the study of certain novel combinatorial aspects of Kekulé counts. The graph- generating character reported here is closely related to the recent work of Randić, Woodworth, Kleiner and Hosoya.
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El-Basil, S. Kekulé structures as graph generators. J Math Chem 14, 305–318 (1993). https://doi.org/10.1007/BF01164473
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DOI: https://doi.org/10.1007/BF01164473