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All Pairs of Pentagons in Leapfrog Fullerenes Are Nice

Author

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  • Tomislav Došlić

    (Faculty of Civil Engineering, University of Zagreb, Kačićeva 26, 10000 Zagreb, Croatia)

Abstract

A subgraph H of a graph G with perfect matching is nice if G − V ( H ) has perfect matching. It is well-known that all fullerene graphs have perfect matchings and that all fullerene graphs contain some small connected graphs as nice subgraphs. In this contribution, we consider fullerene graphs arising from smaller fullerenes via the leapfrog transformation, and show that in such graphs, each pair of (necessarily disjoint) pentagons is nice. That answers in affirmative a question posed in a recent paper on nice pairs of odd cycles in fullerene graphs.

Suggested Citation

  • Tomislav Došlić, 2020. "All Pairs of Pentagons in Leapfrog Fullerenes Are Nice," Mathematics, MDPI, vol. 8(12), pages 1-7, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2135-:d:454298
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    References listed on IDEAS

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    1. Denis Sh. Sabirov & Ottorino Ori, 2020. "Skeletal Rearrangements of the C 240 Fullerene: Efficient Topological Descriptors for Monitoring Stone–Wales Transformations," Mathematics, MDPI, vol. 8(6), pages 1-18, June.
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