TY - JOUR
T1 - A complete characterization for k-resonant Klein-bottle polyhexes
AU - Shiu, Wai Chee
AU - Zhang, Heping
N1 - Funding Information:
This work is supported by FRG, Hong Kong Baptist University; NSFC and TRAPOYT.
PY - 2008/1
Y1 - 2008/1
N2 - 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.
AB - 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.
KW - Fullerene
KW - K-resonance
KW - Kekulé structure
KW - Klein bottle polyhex
KW - Toroidal polyhex
UR - http://www.scopus.com/inward/record.url?scp=37549015217&partnerID=8YFLogxK
U2 - 10.1007/s10910-006-9178-6
DO - 10.1007/s10910-006-9178-6
M3 - Journal article
AN - SCOPUS:37549015217
SN - 0259-9791
VL - 43
SP - 45
EP - 59
JO - Journal of Mathematical Chemistry
JF - Journal of Mathematical Chemistry
IS - 1
ER -