Clar and Fries numbers for benzenoids

Jack E. Graver, Elizabeth J. Hartung, Ahmed Y. Souid

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


A Kekulé structure of a benzenoid or a fullerene Γ is a set of edges K such that each vertex of Γ is incident with exactly one edge in K. The set of faces in Γ that have exactly three edges in K are called the benzene faces of K. The Fries number of Γ is the maximum number of benzene faces over all possible Kekulé structures for Γ. The Clar number is the maximum number of independent benzene faces over all possible Kekulé structures for Γ. It is often assumed, but never proved, that some set of independent benzene faces giving the Clar number is a subset of a set of benzene faces giving the Fries number. In Hartung (The Clar structure of fullerenes, Ph.D. Dissertation. Syracuse University, 2012) it is shown that this assumption is false for a large class of fullerenes. In this paper, we prove that this assumption is valid for a large a class of benzenoids.

Original languageEnglish (US)
Pages (from-to)1981-1989
Number of pages9
JournalJournal of Mathematical Chemistry
Issue number8
StatePublished - Sep 1 2013


  • Benzenoids
  • Clar structure
  • Conjugated 6-circuits
  • Fries structure
  • Fullerenes
  • Kekulé structure

ASJC Scopus subject areas

  • Chemistry(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Clar and Fries numbers for benzenoids'. Together they form a unique fingerprint.

Cite this