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Cyclic edge-cuts in fullerene graphs

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Abstract

In this paper, we study cyclic edge-cuts in fullerene graphs. First, we show that the cyclic edge-cuts of a fullerene graph can be constructed from its trivial cyclic 5- and 6-edge-cuts using three basic operations. This result immediatelly implies the fact that fullerene graphs are cyclically 5-edge-connected. Next, we characterize a class of nanotubes as the only fullerene graphs with non-trivial cyclic 5-edge-cuts. A similar result is also given for cyclic 6-edge-cuts of fullerene graphs.

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Authors and Affiliations

  1. Institute of Mathematics, Faculty of Science, P. J. Šafárik University, Jesenná 5, Košice, 04154, Slovakia

    František Kardoš

  2. Department of Mathematics, University of Ljubljana, Jadranska 19, Ljubljana, 1111, Slovenia

    Riste Škrekovski

Authors
  1. František Kardoš
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  2. Riste Škrekovski
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Correspondence to František Kardoš.

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Kardoš, F., Škrekovski, R. Cyclic edge-cuts in fullerene graphs. J Math Chem 44, 121–132 (2008). https://doi.org/10.1007/s10910-007-9296-9

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  • DOI: https://doi.org/10.1007/s10910-007-9296-9

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