Labeling of Benzenoid Systems which Reflects the Vertex-Distance Relations

It is shown that the vertices of benzenoid systems admit a labeling which reflects their distance relations. To every vertex of a molecular graph of a benzenoid hydrocarbon a sequence of zeros and ones (a binary number) can be associated, such that the number of positions in which these sequences differ is equal to the graph-theoretic vertex distance. It is shown by an example that such labelings can be used not only for nomenclature purposes but also for fast evaluation of molecular parameters based on the graph distance.

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