Kekulé structures and the face independence number of a fullerene

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Abstract

We explore the relationship between Kekulé structures and maximum face independence sets in fullerenes: plane trivalent graphs with pentagonal and hexagonal faces. For the class of leap-frog fullerenes, we show that a maximum face independence set corresponds to a Kekulé structure with a maximum number of benzene rings and may be constructed by partitioning the pentagonal faces into pairs and 3-coloring the faces with the exception of a very few faces along paths joining paired pentagons. We also obtain some partial results for non-leap-frog fullerenes.

Original languageEnglish (US)
Pages (from-to)1115-1130
Number of pages16
JournalEuropean Journal of Combinatorics
Volume28
Issue number4
DOIs
StatePublished - May 1 2007

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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