Internal Kekulé structures for graphene and general patches

Jack E. Graver, Elizabeth J. Hartung

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


A patch is a plane graph whose boundary is an elementary circuit with only vertices of degree 2 or 3, with all degree-2 vertices restricted to the boundary. A Kekulé structure for a patch is a perfect matching. Not all patches admit a perfect matching; in this paper, we define internal Kekulé structures, which match all degree-3 vertices but not necessarily all degree-2 vertices. We consider internal Kekulé structures for general patches to determine what properties of Kekulé structures on hexagonal or graphene patches can be generalized to arbitrary patches, and when a graphene patch with a few defective (non-hexagonal) faces in the interior still "behaves like graphene" away from the defects.

Original languageEnglish (US)
Pages (from-to)693-705
Number of pages13
Issue number3
StatePublished - 2016

ASJC Scopus subject areas

  • General Chemistry
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics


Dive into the research topics of 'Internal Kekulé structures for graphene and general patches'. Together they form a unique fingerprint.

Cite this