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New upper bounds on Zagreb indices

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Abstract

The first Zagreb index M 1(G) is equal to the sum of squares of the degrees of the vertices, and the second Zagreb index M 2(G) is equal to the sum of the products of the degrees of pairs of adjacent vertices of the underlying molecular graph G. In this paper we obtain an upper bound on the first Zagreb index M 1(G) of G in terms of the number of vertices (n), number of edges (m), maximum vertex degree (Δ1), second maximum vertex degree (Δ2) and minimum vertex degree (δ). Using this result we find an upper bound on M 2(G). Moreover, we present upper bounds on \({M_1(G)+M_1(\overline{G})}\) and \({M_2(G)+M_2(\overline{G})}\) in terms of n,  m, Δ1, Δ2, δ, where \({\overline{G}}\) denotes the complement of G.

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References

  1. Gutman I., Trinajstić N.: Chem. Phys. Lett. 17, 535 (1972)

    Article  CAS  Google Scholar 

  2. Gutman I., Ruščić B., Trinajstić N., Wilcox C.F.: J. Chem. Phys. 62, 3399 (1975)

    Article  CAS  Google Scholar 

  3. Nikolić S., Kovačević G., Milićević A., Trinajstić N.: Croat. Chem. Acta. 76, 113 (2003)

    Google Scholar 

  4. Chen S., Xia F.: MATCH Commun. Math. Comput. Chem. 58, 663 (2007)

    Google Scholar 

  5. Das K.C.: Discr. Math. 285, 57 (2004)

    Article  Google Scholar 

  6. Das K.C., Gutman I.: MATCH Commun. Math. Comput. Chem. 52, 103 (2004)

    CAS  Google Scholar 

  7. Zhou B.: MATCH Commun. Math. Comput. Chem. 52, 113 (2004)

    CAS  Google Scholar 

  8. Zhang L., Wu B.: MATCH Commun. Math. Comput. Chem. 54, 189 (2005)

    CAS  Google Scholar 

  9. Zhou B., Gutman I.: MATCH Commun. Math. Comput. Chem. 54, 233 (2005)

    CAS  Google Scholar 

  10. Kumar V., Madan A.K.: J. Math. Chem. 42, 925 (2007)

    Article  CAS  Google Scholar 

  11. Zhou B.: MATCH Commun. Math. Comput. Chem. 57, 591 (2007)

    CAS  Google Scholar 

  12. Deng H.: MATCH Commun. Math. Comput. Chem. 57, 597 (2007)

    CAS  Google Scholar 

  13. Zhou B.: Int. J. Quantum Chem. 107, 875 (2007)

    Article  CAS  Google Scholar 

  14. Yan Z., Liu H., Liu H.: J. Math. Chem. 42, 565 (2007)

    Article  CAS  Google Scholar 

  15. Estrada E., Matamala A.R.: J. Math. Chem. 43, 508 (2008)

    Article  CAS  Google Scholar 

  16. Zhou B., Trinajstić N.: J. Math. Chem. 44, 235 (2008)

    Article  CAS  Google Scholar 

  17. Balaban A.T., Motoc I., Bonchev D., Mekenyan O.: Topics Curr. Chem. 114, 21 (1983)

    Article  CAS  Google Scholar 

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

    Book  Google Scholar 

Download references

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Authors and Affiliations

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

    Kinkar Ch. Das

  2. Faculty of Science, University of Kragujevac, B.O. Box 60, Kragujevac, 34000, Serbia

    Ivan Gutman

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

    Bo Zhou

Authors
  1. Kinkar Ch. Das
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  2. Ivan Gutman
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  3. Bo Zhou
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Correspondence to Ivan Gutman.

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Das, K.C., Gutman, I. & Zhou, B. New upper bounds on Zagreb indices. J Math Chem 46, 514–521 (2009). https://doi.org/10.1007/s10910-008-9475-3

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  • DOI: https://doi.org/10.1007/s10910-008-9475-3

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