A relation between clar covering polynomial and cube polynomial

Heping Zhang, Wai Chee Shiu*, Pak Kiu Sun

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

20 Citations (Scopus)


The Clar covering polynomial (Zhang-Zhang polynomial) of a hexagonal system is a counting polynomial of resonant structures called Clar covers, which can be used to determine the Kekulé count, the first Herndon number and Clar number. In this paper we prove that the Clar covering polynomial of a hexagonal system H coincides with the cube polynomial of its resonance graph R(H) by establishing a bijection between the Clar covers of H and the hypercubes in R(H). Moreover, some important applications of this relation are presented.

Original languageEnglish
Pages (from-to)477-492
Number of pages16
JournalMATCH Communications in Mathematical and in Computer Chemistry
Issue number2
Publication statusPublished - 2013

Scopus Subject Areas

  • Chemistry(all)
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics


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