A complete characterization for k-resonant Klein-bottle polyhexes

Wai Chee SHIU*, Heping Zhang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

22 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)45-59
Number of pages15
JournalJournal of Mathematical Chemistry
Issue number1
Publication statusPublished - Jan 2008

Scopus Subject Areas

  • Chemistry(all)
  • Applied Mathematics

User-Defined Keywords

  • Fullerene
  • K-resonance
  • Kekulé structure
  • Klein bottle polyhex
  • Toroidal polyhex


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