Abstract
A (3,6)-fullerene G is a plane cubic graph whose faces are only triangles and hexagons. It follows from Euler’s formula that the number of triangles is four. A face of G is called resonant if its boundary is an alternating cycle with respect to some perfect matching of G. In this paper, we show that every hexagon of a (3,6)-fullerene G with connectivity 3 is resonant except for one graph, and there exist a pair of disjoint hexagons in G that are not mutually resonant except for two trivial graphs without disjoint hexagons. For any (3,6)-fullerene with connectivity 2, we show that it is composed of n(n ≥ 1) concentric layers of hexagons, capped on each end by a cap formed by two adjacent triangles, and none of its hexagons is resonant.
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Yang, R., Zhang, H. Hexagonal resonance of (3,6)-fullerenes. J Math Chem 50, 261–273 (2012). https://doi.org/10.1007/s10910-011-9910-8
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DOI: https://doi.org/10.1007/s10910-011-9910-8