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Wiener, hyper-Wiener, detour and hyper-detour indices of bridge and chain graphs

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Abstract

Given a collection of connected graphs one may build bridge and chain graphs out of them. In this paper it is shown how the Wiener, hyper-Wiener, detour and hyper-detour indices for bridge and chain graphs are determined from the respective indices of the individual graphs. The results obtained are illustrated by some examples.

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References

  1. Amić D., Trinajstić N.: Croat. Chem. Acta 68, 53–62 (1995)

    Google Scholar 

  2. Balakrishnan R., Sridharan N., Viswanathan Iyer K.: Appl. Math. Lett. 21, 922–927 (2008)

    Article  Google Scholar 

  3. F. Buckley, F. Harary, Distance in Graphs. (Addison-Wesley, Reading, 1990)

  4. D.M. Cvetkovic, M. Doob, H. Sachs, Spectra of Graphs, (Academic Press, 1980)

  5. M.V. Diudea, I. Gutman, J. Lorentz, Molecular Topology. (Nova Science Publishers, 2001)

  6. C. Godsil, G. Royle, Algebraic Graph Theory. (Springer, 2004)

  7. Gutman I., Dobrynin A.A.: The Szeged index—a success story. Graph Theor. Notes N. Y. 34, 37–44 (1998)

    Google Scholar 

  8. I. Gutman, S. Klavzar, B. Mohar (eds.), Fifty years of the Wiener index. MATCH Commun. Math. Chem. 35, 1–259 (1997)

  9. Gutman I., Linert W., Lukovits I., Dobrynin A.A.: J. Chem. Inf. Comput. Sci. 37, 349–354 (1997)

    CAS  Google Scholar 

  10. F. Harary, Graph Theory, (Addison-Wesley, Reading, 1969)

  11. Ivanciue O., Trinajstić N.: Commun. Math. Comput. Chem. 30, 141–1522 (1994)

    Google Scholar 

  12. Khadikar P.V.: Natl. Acad. Sci. Lett. 23, 113–118 (2000)

    CAS  Google Scholar 

  13. Khadikar P.V., Deshpande N.V., Kale P.P., Dobrynin A., Gutman I.: J. Chem. Inf. Comput. Sci. 35, 547–550 (1995)

    CAS  Google Scholar 

  14. Khadikar P.V., Karmarkar S., Agrawal V.K.: Natl. Acad. Sci. Lett. 23, 165–170 (2000)

    CAS  Google Scholar 

  15. Klein D.J., Lukovits I., Gutman I.: J. Chem. Inf. Comput. Sci. 35, 50–52 (1995)

    CAS  Google Scholar 

  16. Lukovits I.: Comput. Chem. 19, 27–31 (1995)

    Article  CAS  Google Scholar 

  17. Lukovits I.: Croat. Chem. Acta 69, 873–882 (1996)

    CAS  Google Scholar 

  18. Lukovits I., Razinger M.: J. Chem. Inf. Comput. Sci. 37, 283–286 (1997)

    CAS  Google Scholar 

  19. Mansour T., Schork M.: MATCH Commun. Math. Chem. 61, 723–734 (2009)

    Google Scholar 

  20. T. Mansour, M. Schork, Discret. Appl. Math. (to appear)

  21. Randić M.: Chem. Phys. Lett. 211, 478–483 (1993)

    Article  Google Scholar 

  22. Randić M., DeAlba L.M., Harris F.E.: Crat. Chem. Acta 71, 53–68 (1998)

    Google Scholar 

  23. Trinajstić N.: Chemical Graph Theory. CRC Press, Boca Raton (1983)

    Google Scholar 

  24. Trinajstić N., Nikolić S., Luc̆ić B., Amić D., Mihalić Z.: J. Chem. Inf. Comput. Sci. 37, 631–638 (1997)

    Google Scholar 

  25. Trinajstić N., Nikolić S., Mihalić Z.: Int. J. Quantum Chem.: Quantum Chem. Symp. 65, 415–419 (1997)

    Article  Google Scholar 

  26. Wiener H.: J. Am. Chem. Soc. 69, 17–20 (1947)

    Article  CAS  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, University of Haifa, 31905, Haifa, Israel

    Toufik Mansour & Matthias Schork

  2. Camillo-Sitte-Weg 25, 60488, Frankfurt, Germany

    Toufik Mansour & Matthias Schork

Authors
  1. Toufik Mansour
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  2. Matthias Schork
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Correspondence to Toufik Mansour.

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Mansour, T., Schork, M. Wiener, hyper-Wiener, detour and hyper-detour indices of bridge and chain graphs. J Math Chem 47, 72–98 (2010). https://doi.org/10.1007/s10910-009-9531-7

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  • DOI: https://doi.org/10.1007/s10910-009-9531-7

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