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On the anti-Kekulé number of leapfrog fullerenes

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Abstract

The Anti-Kekulé number of a connected graph G is the smallest number of edges that have to be removed from G in such way that G remains connected but it has no Kekulé structures. In this paper it is proved that the Anti-Kekulé number of all fullerenes is either 3 or 4 and that for each leapfrog fullerene the Anti-Kekulé number can be established by observing finite number of cases not depending on the size of the fullerene.

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Authors and Affiliations

  1. University of Primorska, Cankarjeva 6, 6000, Koper, Slovenia

    Klavdija Kutnar

  2. Faculty of Civil Engineering and Architecture, University of Split, Matice Hrvatske 15, 21000, Split, Croatia

    Jelena Sedlar

  3. Department of Mathematics, University of Split, Nikole Tesle 12, 21000, Split, Croatia

    Damir Vukičević

Authors
  1. Klavdija Kutnar
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  2. Jelena Sedlar
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  3. Damir Vukičević
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Corresponding author

Correspondence to Damir Vukičević.

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Kutnar, K., Sedlar, J. & Vukičević, D. On the anti-Kekulé number of leapfrog fullerenes. J Math Chem 45, 431–441 (2009). https://doi.org/10.1007/s10910-008-9416-1

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  • DOI: https://doi.org/10.1007/s10910-008-9416-1

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