Kekuléan benzenoids

Jack E. Graver, Elizabeth J. Hartung

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

A Kekulé structure for 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, i.e. a perfect matching. All fullerenes admit a Kekulé structure; however, this is not true for benzenoids. In this paper, we develop methods for deciding whether or not a given benzenoid admits a Kekulé structure by constructing Kekulé structures that have a high density of benzene rings. The benzene rings of the Kekulé structure K are the faces in Γ that have exactly three edges in K. The Fries number of Γ is the maximum number of benzene rings over all possible Kekulé structures for Γ and the set of benzene rings giving the Fries number is called a Fries set. The Clar number is the maximum number of independent benzene rings over all possible Kekulé structures for Γ and the set of benzene rings giving the Clar number is called a Clar set. Our method of constructing Kekulé structures for benzenoids generally gives good estimates for the Clar and Fries numbers, often the exact values.

Original languageEnglish (US)
Pages (from-to)977-989
Number of pages13
JournalJournal of Mathematical Chemistry
Volume52
Issue number3
DOIs
StatePublished - Mar 1 2014

Keywords

  • Benzene faces
  • Benzene rings
  • Benzenoids
  • Clar number
  • Conjugated 6-circuits
  • Fries number
  • Fullerenes
  • Graphene patches
  • Kekulé structure

ASJC Scopus subject areas

  • Chemistry(all)
  • Applied Mathematics

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