k-resonant toroidal polyhexes |
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Authors: | Heping Zhang Dong Ye |
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Institution: | (1) School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, P.R. China |
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Abstract: | A toroidal polyhex H(p, q, t) is a cubic bipartite graph embedded on the torus such that each face is a hexagon, which can be described by a string (p, q, t) of three integers (p≥ 1, q≥ 1, 0≤ t≤ p−1). A set of mutually disjoint hexagons of H(p, q, t) is called a resonant pattern if H(p, q, t) has a prefect matching M such that all haxgons in are M-alternating. A toroidal polyhex H(p, q, t) is k-resonant if any i (1 ≤ i ≤ k) mutually disjoint hexagons form a resonant pattern. In 16], Shiu, Lam and Zhang characterized 1, 2 and 3-resonant toroidal
polyhexes H(p, q, t) for min(p, q)≥ 2. In this paper, we characterize k-resonant toroidal polyhexes H(p, 1, t). Furthermore, we show that a toroidal polyhex H(p, q, t) is k-resonant (k≥ 3) if and only if it is 3-resonant.
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Keywords: | Toroidal polyhex Perfect matching Resonant pattern k-resonant |
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