Abstract
A benzenoid systemH is a finite connected subgraph of the infinite hexagonal lattice with out cut bonds and non-hexagonal interior faces. The branching graphG ofH consists of all vertices ofH of degree 3 and bonds among them. In this paper, the following results are obtained:
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(1)
A necessary condition for a benzenoid system to have a Hamiltonian circuit.
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(2)
A necessary and sufficient condition for a benzenoid system to have a Hamiltonian path.
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(3)
A characterization of connected subgraphs of the infinite hexagonal lattice which are branching graphs of benzenoid systems.
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(4)
A proof that if a disconnected subgraph G of the infinite hexagonal lattice given along with the positions of its vertices is the branching graph of a benzenoid system H, then H is unique.
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Hansen, P., Zheng, M. Hamiltonian circuits, Hamiltonian paths and branching graphs of benzenoid systems. J Math Chem 17, 15–33 (1995). https://doi.org/10.1007/BF01165135
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DOI: https://doi.org/10.1007/BF01165135