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A new algorithm for computing distance matrix and Wiener index of zig-zag polyhex nanotubes

AliReza Ashrafi1* and Shahram Yousefi2

Author Affiliations

1 Institute for Nanoscience and Nanotechnology, University of Kashan, Kashan, Iran

2 Center for Space Studies, Malek-Ashtar University of Technology, Tehran, Iran

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Nanoscale Research Letters 2007, 2:202-206  doi:10.1007/s11671-007-9051-y

The electronic version of this article is the complete one and can be found online at:

Received:31 December 2006
Accepted:20 February 2007
Published:10 April 2007

© 2007 to the authors


The Wiener index of a graph G is defined as the sum of all distances between distinct vertices of G. In this paper an algorithm for constructing distance matrix of a zig-zag polyhex nanotube is introduced. As a consequence, the Wiener index of this nanotube is computed.

Zig-zag polyhex nanotube; Distance matrix; Wiener index

Nano Express



We would like to thank from referees for their helpful remarks and suggestions. This work was partially supported by the Center of Excellence of Algebraic Methods and Applications of the Isfahan University of Technology.


  1. Todeschini R, Consonni V: Handbook of Molecular Descriptors. Wiley, Weinheim; 2000. OpenURL

  2. Trinajstic N: Chemical Graph Theory. CRC Press, Boca Raton, FL; 1983. OpenURL

  3. Wiener H:

    J. Am. Chem. Soc.. 1947, 69:17.

    COI number [1:CAS:528:DyaH2sXpt1Sj]

    Publisher Full Text OpenURL

  4. Hosoya H:

    Bull. Chem. Soc. Japan. 1971, 44:2332.

    COI number [1:CAS:528:DyaE3MXlsVSis78%3D]

    Publisher Full Text OpenURL

  5. Dobrynin AA:

    Comput. Chem.. 1999, 23:43.

    COI number [1:CAS:528:DyaK1MXhtVKlur8%3D]

    Publisher Full Text OpenURL

  6. Dobrynin AA, Entringer R, Gutman I:

    Acta Appl. Math.. 2001, 66:211. Publisher Full Text OpenURL

  7. Dobrynin AA, Gutman I, Klavžar S, Zigert P:

    Acta Appl. Math.. 2002, 72:247. Publisher Full Text OpenURL

  8. Gutman I, Körtvélyesi T:

    Z. Naturforsch.. 1995, 50a:669. OpenURL

  9. John PE, Diudea MV:

    Croat. Chem. Acta. 2004, 77:127.

    COI number [1:CAS:528:DC%2BD2cXmtFSrtLc%3D]


  10. Diudea MV, Stefu M, Pârv B, John PE:

    Croat. Chem. Acta. 2004, 77:111.

    COI number [1:CAS:528:DC%2BD2cXmtFSrtLk%3D]


  11. Diudea MV:

    J. Chem. Inf. Model.. 2005, 45:1002.

    COI number [1:CAS:528:DC%2BD2MXktF2ltb0%3D]

    Publisher Full Text OpenURL

  12. Diudea MV:

    J. Chem. Inf. Comput. Sci.. 1996, 36:833.

    COI number [1:CAS:528:DyaK28XjvFWlu7w%3D]

    Publisher Full Text OpenURL

  13. Diudea MV, Graovac A:

    MATCH Commun. Math. Comput. Chem.. 2001, 44:93.

    COI number [1:CAS:528:DC%2BD38XkvFOgtw%3D%3D]


  14. Diudea MV, Silaghi-Dumitrescu I, Parv B:

    MATCH Commun. Math. Comput. Chem.. 2001, 44:117.

    COI number [1:CAS:528:DC%2BD38XkvFOgug%3D%3D]


  15. Diudea MV, John PE:

    MATCH Commun. Math. Comput. Chem.. 2001, 44:103.

    COI number [1:CAS:528:DC%2BD38XkvFOgtQ%3D%3D]


  16. Yousefi S, Ashrafi AR:

    MATCH Commun. Math. Comput. Chem.. 2006, 56:169.

    COI number [1:CAS:528:DC%2BD2sXhs1aksbo%3D]


  17. Ashrafi AR, Yousefi S:

    MATCH Commun. Math. Comput. Chem.. 2007, 57:403.

    COI number [1:CAS:528:DC%2BD2sXls12lt7s%3D]


  18. Cameron PJ: Combinatorics: Topics, Techniques, Algorithms. Cambridge University Press, Cambridge; 1994. OpenURL