Normal components, Kekulé patterns, and Clar patterns in plane bipartite graphs

Wai Chee Shiu*, Peter Che Bor Lam, Fuji Zhang, Heping Zhang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

20 Citations (Scopus)
8 Downloads (Pure)


As a general case of molecular graphs of polycyclic alternant hydrocarbons, we consider a plane bipartite graph G with a Kekulé pattern (perfect matching). An edge of G is called nonfixed if it belongs to some, but not all, perfect matchings of G. Several criteria in terms of resonant cells for determining whether G is elementary (i.e., without fixed edges) are reviewed. By applying perfect matching theory developed in plane bipartite graphs, in a unified and simpler way we study the decomposition of plane bipartite graphs with fixed edges into normal components, which is shown useful for resonance theory, in particular, cell and sextet polynomials. Further correspondence between the Kekulé patterns and Clar (resonant) patterns are revealed.

Original languageEnglish
Pages (from-to)405-420
Number of pages16
JournalJournal of Mathematical Chemistry
Issue number4
Publication statusPublished - May 2002

Scopus Subject Areas

  • Chemistry(all)
  • Applied Mathematics

User-Defined Keywords

  • benzenoid
  • Kekulé structure
  • Clar pattern
  • plane bipartite graph
  • normal component


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