Similarity and a duality for fullerenes

Jennifer J. Edmond, Jack E. Graver

Research output: Contribution to journalArticlepeer-review


Fullerenes are molecules of carbon that are modeled by trivalent plane graphs with only pentagonal and hexagonal faces. Scaling up a fullerene gives a notion of similarity, and fullerenes are partitioned into similarity classes. In this expository article, we illustrate how the values of two important fullerene parameters can be deduced for all fullerenes in a similarity class by computing the values of these parameters for just the three smallest representatives of that class. In addition, it turns out that there is a natural duality theory for similarity classes of fullerenes based on one of the most important fullerene construction techniques: leapfrog construction. The literature on fullerenes is very extensive, and since this is a general interest journal, we will summarize and illustrate the fundamental results that we will need to develop similarity and this duality.

Original languageEnglish (US)
Pages (from-to)2047-2061
Number of pages15
Issue number4
StatePublished - 2015


  • Clar number
  • Fries number
  • Fullerene
  • Leapfrog construction

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • General Mathematics
  • Physics and Astronomy (miscellaneous)


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