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Bounds on Harary index

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Abstract

In this paper, we obtain the lower and upper bounds on the Harary index of a connected graph (molecular graph), and, in particular, of a triangle- and quadrangle-free graphs in terms of the number of vertices, the number of edges and the diameter. We give the Nordhaus–Gaddum-type result for Harary index using the diameters of the graph and its complement. Moreover, we compare Harary index and reciprocal complementary Wiener number for graphs.

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References

  1. Plavšić D., Nikolić S., Trinajstić N., Mihalić Z.: On the Harary index for the characterization of chemical graphs. J. Math. Chem. 12, 235–250 (1993)

    Article  Google Scholar 

  2. Ivanciuc O., Balaban T.S., Balaban A.T.: Reciprocal distance matrix, related local vertex invariants and topological indices. J. Math. Chem. 12, 309–318 (1993)

    Article  CAS  Google Scholar 

  3. D. Janežič, A. Miličević, S. Nikolić, N. Trinajstić, Graph Theoretical Matrices in Chemistry, Mathematical Chemistry Monographs No. 3, University of Kragujevac, Kragujevac (2007)

  4. Hosoya H.: Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons. Bull. Chem. Soc. Jpn. 44, 2332–2339 (1971)

    CAS  Google Scholar 

  5. Wiener H.: Structural determination of paraffin boiling points. J. Am. Chem. Soc. 69, 17–20 (1947)

    Article  CAS  Google Scholar 

  6. Ivanciuc O., Ivanciuc T., Balaban A.T.: Design of topological indices. Part 10. Parameters based on electronegativity and vovalent radius for the computation of molecular graph descriptors for heteroatom-containing molecules. J. Chem. Inf. Comput. Sci. 38, 395–495 (1998)

    CAS  Google Scholar 

  7. Diudea M.V.: Indices of reciprocal properties or Harary indices. J. Chem. Inf. Comput. Sci. 37, 292–299 (1997)

    CAS  Google Scholar 

  8. Lučić B., Miličević A., Nikolić S., Trinajstić N.: Harary index-twelve years later. Croat. Chem. Acta 75, 847–868 (2002)

    Google Scholar 

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

    Google Scholar 

  10. Todeschini R., Consonni V.: Handbook of Molecular Descriptors. Weinheim, Wiley-VCH (2000)

    Book  Google Scholar 

  11. Mihalić Z., Trinajstić N.: A graph-theoretical approach to structure-property relationships. J. Chem. Educ. 69, 701–712 (1999)

    Article  Google Scholar 

  12. Ivanciuc O.: QSAR comparative study of Wiener descriptors for weighted molecular graphs. J. Chem. Inf. Comput. Sci. 40, 1412–1422 (2000)

    CAS  Google Scholar 

  13. Trinajstić N., Nikolić S., Basak S.C., Lukovits I.: Distance indices and their hyper-counterparts: intercorrelation and use in the structure-property modeling. SAR QSAR Environ. Res. 12, 31–54 (2001)

    Article  Google Scholar 

  14. Zhou B., Cai X., Trinajstić N.: On Harary index. J. Math. Chem. 44, 611–618 (2008)

    Article  CAS  Google Scholar 

  15. B. Zhou, X. Cai, N. Trinajstić, On reciprocal complementary Wiener number. Discrete Appl. Math. (in press). doi:10.1016/j.dam.2008.09.010

  16. Trinajstić N.: Chemical Graph Theory, 2nd revised edn. CRC Press, Boca Raton (1992)

    Google Scholar 

  17. Gutman I., Trinajstić N.: Graph theory and molecular orbitals. III. Total π-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17, 535–538 (1972)

    CAS  Google Scholar 

  18. Gutman I., Ruščić B., Trinajstić N., Wilcox C.F. Jr.: Graph theory and molecular orbitals. XII. Acyclic polyenes. J. Chem. Phys. 62, 3399–3405 (1975)

    Article  CAS  Google Scholar 

  19. Nikolić S., Kovačević G., Mihalić A., Trinajstić N.: The Zagreb indices 30 years after. Croat. Chem. Acta 76, 113–124 (2003)

    Google Scholar 

  20. Gutman I., Das K.C.: first Zagreb index 30 years after. MATCH Commun. Math. Comput. Chem. 50, 83–92 (2004)

    CAS  Google Scholar 

  21. Zhou B., Stevanović D.: A note on Zagreb indices. MATCH Commun. Math. Comput. Chem. 56, 571–578 (2006)

    CAS  Google Scholar 

  22. K.C. Das, I. Gutman, B. Zhou, New upper bounds on Zagreb indices. J. Math. Chem. doi:10.1007/s10910-008-9475-3

  23. Cvetković D.M., Doob M., Sachs H.: Spectra of Graphs-Theory and Application. Johann Ambrosius Barth, Heidelberg (1995)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, Republic of Korea

    Kinkar Ch. Das

  2. Department of Mathematics, South China Normal University, Guangzhou, 510631, People’s Republic of China

    Bo Zhou

  3. The Rugjer Bošković Institute, 10002, Zagreb, Croatia

    N. Trinajstić

Authors
  1. Kinkar Ch. Das
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  2. Bo Zhou
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  3. N. Trinajstić
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Correspondence to Kinkar Ch. Das.

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Das, K.C., Zhou, B. & Trinajstić, N. Bounds on Harary index. J Math Chem 46, 1377–1393 (2009). https://doi.org/10.1007/s10910-009-9522-8

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  • DOI: https://doi.org/10.1007/s10910-009-9522-8

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