On the Clar number of graphene fragment

Abstract

A graphene fragment is a benzenoid graph that its dualist graph is a unicyclic graph. In particular, when the dualist graph of a benzenoid graph is a circle, it is called cyclofusene. In this paper, we determine the Clar number of a cyclofusene graph, and prove a bound for the Clar number of the graphene fragment. Moreover, we construct the graphene fragment which can attain this bound. More precisely, it is shown that the Clar number of the graphene fragment with n hexagons is at most \([\frac{2n}{3}]\).

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Acknowledgements

The authors are grateful to the referees for their valuable comments and helpful suggestions in improving the presentation of this manuscript.

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Correspondence to Biao Zhao.

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Tian, Y., Zhao, B. On the Clar number of graphene fragment. J Math Chem 59, 542–553 (2021). https://doi.org/10.1007/s10910-021-01214-w

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Keywords

  • Clar number
  • Benzenoid graph
  • Graphene fragment