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Hamiltonian paths in polyhexes: The use of branching subgraphs to assist diagnosis of graph traceability

  • Section A / Arenes and Aromaticity
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Abstract

The traceability of some of the smaller polyhexes is examined. (A graph is said to be traceable or to have a Hamiltonian path if it has a path visiting every vertex just once.) Most polyhexes are traceable, and an attempt is made to develop some practical guidelines for finding those that are not. A subgraph consisting of the branching vertices of a polyhex, and of any edges which join pairs of such vertices, is a useful tool for this purpose. The “principal resonance structures” of such a graph suggest ways of finding simpler spannng subgraphs of the polyhex that will often make its traceability, or lack of it, more obvious.

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  1. Resource Use Institute, 14 Lower Oakfield, PH16 5DS, Pitlochry, Perthshire, Scotland, UK

    E. C. Kirby

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Kirby, E.C. Hamiltonian paths in polyhexes: The use of branching subgraphs to assist diagnosis of graph traceability. J Math Chem 4, 31–46 (1990). https://doi.org/10.1007/BF01170002

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