Abstract:A catacondensed polyhex H is a connected subgraph of a hexagonal system such that any edge of H lies in a hexagon of H, any triple of hexagons of H has an empty intersection and the inner dual of H is a cactus graph. A perfect matching M of a catacondensed polyhex H is relevant if every cycle of the inner dual of H admits a vertex that corresponds to the hexagon which contributes three edges in M. The vertex set of the graph R˜(H) consists of all relevant perfect matchings of H, two perfect matchings being adj… Show more
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