Department of Mathematics
A complete characterization for k-resonant Klein-bottle polyhexes
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. © 2006 Springer Science+Business Media, Inc.
Fullerene, K-resonance, Kekulé structure, Klein bottle polyhex, Toroidal polyhex
Source Publication Title
Journal of Mathematical Chemistry
Shiu, Wai Chee, and Heping Zhang. "A complete characterization for k-resonant Klein-bottle polyhexes." Journal of Mathematical Chemistry 43.1 (2008): 45-59.