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Finding more perfect matchings in leapfrog fullerenes

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Abstract

We use some recent results on the existence of long cycles in leapfrog fullerenes to establish new exponential lower bounds on the number of perfect matchings in such graphs. The new bounds are expressed in terms of Fibonacci numbers.

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References

  1. Austin S.J., Fowler P.W., Hansen P., Manolopoulos D.E., Zheng M.: Fullerene isomers of C 60: Kekulé counts versus stability. Chem. Phys. Lett. 228, 478 (1994)

    Article  CAS  Google Scholar 

  2. Cyvin S.J., Gutman I.: in Kekulé Structures in Benzenoid Hydrocarbons, Lect. Notes Chem. 46. Springer, Heidelberg (1988)

    Google Scholar 

  3. Došlić T.: On lower bounds of number of perfect matchings in fullerene graphs. J. Math. Chem. 24, 359 (1998)

    Article  Google Scholar 

  4. Došlić T.: On some structural properties of fullerene graphs. J. Math. Chem. 31, 187 (2002)

    Article  Google Scholar 

  5. Došlić T.: Importance and redundancy in fullerene graphs. Croat. Chem. Acta 75, 869 (2002)

    Google Scholar 

  6. Došlić T.: Cyclical edge-connectivity of fullerene graphs and (k, 6)-cages. J. Math. Chem. 33, 103 (2003)

    Article  Google Scholar 

  7. Došlić T.: Fullerene graphs with exponentially many perfect matchings. J. Math. Chem. 41, 183 (2007)

    Article  Google Scholar 

  8. Došlić T.: Leapfrog fullerenes have many perfect matchings. J. Math. Chem. 44, 1 (2008)

    Article  Google Scholar 

  9. Fowler P.W., Pisanski T.: Leapfrog transformations and polyhedra of Clar type. J. Chem. Soc. Faraday Trans. 90, 2865 (1994)

    Article  CAS  Google Scholar 

  10. Fowler P.W., Manolopoulos D.E.: in An Atlas of Fullerenes. Clarendon Press, Oxford (1995)

    Google Scholar 

  11. Grünbaum B., Motzkin T.S.: The number of hexagons and the simplicity of geodesics on certain polyhedra. Can J. Math. 15, 744 (1963)

    Google Scholar 

  12. Harary F.: in Graph Theory. Addison-Wesley, Reading, MA (1969)

    Google Scholar 

  13. Klein D.J., Liu X.: Theorems for carbon cages. J. Math. Chem. 11, 199 (1992)

    Article  CAS  Google Scholar 

  14. Kutnar K., Marušič D.: On cyclic edge connectivity of fullerenes. . Discrete Appl. Math. 156, 1661 (2008)

    Article  Google Scholar 

  15. K. Kutnar, D. Marušič, D. Vukičević, On decompositions of leapfrog fullerenes, J. Math. Chem. doi:10.1007/s10910-008-9414-3

  16. Lovász L., Plummer M.D.: in Matching Theory. North-Holland, Amsterdam (1986)

    Google Scholar 

  17. Marušič D.: Hamilton cycles and paths in fullerenes. J. Chem. Inf. Model. 47, 732 (2007)

    Article  Google Scholar 

  18. Payan C., Sakarovitch M.: Ensembles cycliquement et graphes cubiques. Cahiers du Centre dÉtudes Rech. Opérationnelle 17, 319 (1975)

    Google Scholar 

  19. Qi Z., Zhang H.: A note on the cyclical edge-connectivity of fullerene graphs. J. Math. Chem. 43, 134 (2008)

    Article  CAS  Google Scholar 

  20. Quian J., Zhang F.: On the number of Kekulé structures in capped zigzag nanotubes. J. Math. Chem. 38, 233 (2005)

    Article  Google Scholar 

  21. West D.B.: in Introduction to Graph Theory. Prentice Hall, Upper Saddle River, NJ (1996)

    Google Scholar 

  22. Zhang H., Zhang F.: New lower bounds on the number of perfect matchings of fullerene graphs. J. Math. Chem. 30, 343 (2001)

    Article  CAS  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Civil Engineering, University of Zagreb, Kačićeva 26, 10000, Zagreb, Croatia

    Tomislav Došlić

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  1. Tomislav Došlić
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Correspondence to Tomislav Došlić.

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Došlić, T. Finding more perfect matchings in leapfrog fullerenes. J Math Chem 45, 1130–1136 (2009). https://doi.org/10.1007/s10910-008-9435-y

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  • DOI: https://doi.org/10.1007/s10910-008-9435-y

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