A complete characterization for k-resonant Klein-bottle polyhexes |
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Authors: | Wai Chee Shiu Heping Zhang |
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Affiliation: | (1) Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, 224 Waterloo Road, Kowloon Tong, Hong Kong, P. R. China;(2) School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, P. R. China |
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Abstract: | A hexagonal tessellation K(p, q, t) on Klein bottle, a non-orientable surface with cross-cap number 2, is a finite-sized elemental benzenoid which can be produced from a p × q-parallelogram of hexagonal lattice with usual identifications of sides and with torsion t. Unlike torus, Klein bottle polyhex K(p, q, t) is not transitive except for some degenerated cases. We shall show, however, that K(p, q, t) does not depend on t. Accordingly, criteria for K(p, q, t) to be k-resonant for every positive integer k will be given. Moreover, we shall show that K(3, q, t) of 3-resonance are fully-benzenoid. |
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Keywords: | Fullerene Klein bottle polyhex toroidal polyhex Kekulé structure k-resonance |
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