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Distances on nanotubical structures

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Abstract

Nanotubical graphs are obtained by wrapping a hexagonal grid into a cylinder, and then possibly closing the tube with patches. In this paper we determine the number of vertices at distance d from a particular vertex in an open (k, l) nanotubical graph. Surprisingly, this number does not depend much on the type of the nanotubical structure, but mainely on its circumference. In particular, for \(d\ge 2k\) it is \(2\,(k+l)\) for an infinite open nanotube. This result can be used as a tool for precise evaluation of distance based topological indices for nanotubical structures. The presented results imply an interesting conclusion that these indices do not distinguish the type of the nanotubes very well.

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References

  1. V. Andova, D. Blenkuš, T. Došlić, F. Kardoš, R. Škrekovski, MATCH Commun. Math. Comput. Chem. 73, 529 (2015)

    Google Scholar 

  2. V. Andova, F. Kardoš, R. Škrekovski, Ars Math. Contempl. 11, 353 (2016)

    Google Scholar 

  3. V. Andova, F. Kardoš, R. Škrekovski, MATCH Commun. Math. Comput. Chem. 73, 501 (2015)

    Google Scholar 

  4. A.T. Balaban, Chem. Phys. Lett. 89, 399 (1982)

    Article  CAS  Google Scholar 

  5. A.T. Balaban, Pure Appl. Chem. 55, 199 (1983)

    Article  CAS  Google Scholar 

  6. G. Brinkmann, A.W.M. Dress, J. Algorithams 23, 345 (1997)

    Article  Google Scholar 

  7. G. Brinkmann, P.W. Fowler, D.E. Manolopoulos, A.H.R. Palser, Chem. Phys. Lett. 315, 335 (1999)

    Article  CAS  Google Scholar 

  8. J. Devillers, A.T. Balaban, Topological Indices and Related Descriptors in QSAR and QSPR (Gordon & Breach, Amsterdam, 1999)

    Google Scholar 

  9. M.S. Dresselhaus, P.C. Eklund, Adv. Phys. 49, 705 (2000)

    Article  CAS  Google Scholar 

  10. T. Došlić, J. Math. Chem. 33, 103 (2003)

    Article  Google Scholar 

  11. G. Grassy, B. Calas, A. Yasri, R. Lahana, J. Woo, S. Iyer, M. Kaczorek, F. Floćh, R. Buelow, Nat. Biotechnol. 16, 748 (1998)

    Article  CAS  Google Scholar 

  12. S. Iijima, Nature 354, 56–58 (1991)

    Article  CAS  Google Scholar 

  13. F.H. Kaatz, A. Bultheel, J. Math. Chem. 51, 1211 (2013)

    Article  CAS  Google Scholar 

  14. H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl, R.E. Smalley, Nature 318, 1623 (1985)

    Article  Google Scholar 

  15. P. Schwerdtfeger, L. Wirz, J. Avery, WIREs Comput. Mol. Sci. 5, 96 (2015). doi:10.1002/wcms.1207

    Article  CAS  Google Scholar 

  16. R. Todeschini, V. Consonni, Handbook of Molecular Descriptors (Wiley, Weinheim, 2000)

    Book  Google Scholar 

  17. H. Wiener, J. Am. Chem. Soc. 1, 17 (1947)

    Article  Google Scholar 

  18. X. Zhao, Y. Liu, S. Inoue, T. Suzuki, R.O. Jones, Y. Ando, Phys. Rev. Lett. 92, 125502-1 (2004)

    Google Scholar 

Download references

Acknowledgments

The second author acknowledges partial support by Slovak research grants VEGA 1/0007/14, VEGA 1/0026/16 and APVV 0136–12. The research was partially supported by Slovenian research agency ARRS, program no. P1–0383 and project no. L1–4292.

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Authors and Affiliations

  1. Faculty of Electrical Engineering and Information Technologies, Ss Cyril and Methodius Univ., Ruger Boskovik 18, 1000, Skopje, Macedonia

    Vesna Andova

  2. Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Bratislava, Slovakia

    Martin Knor

  3. Faculty of Information Studies, Novo mesto, Slovakia

    Riste Škrekovski

  4. Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovakia

    Riste Škrekovski

  5. University of Primorska, FAMNIT, Koper, Slovenia

    Riste Škrekovski

Authors
  1. Vesna Andova
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  2. Martin Knor
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  3. Riste Škrekovski
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Correspondence to Vesna Andova.

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Andova, V., Knor, M. & Škrekovski, R. Distances on nanotubical structures. J Math Chem 54, 1575–1584 (2016). https://doi.org/10.1007/s10910-016-0637-4

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  • DOI: https://doi.org/10.1007/s10910-016-0637-4

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