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Some new lower bounds for augmented Zagreb index

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Abstract

Let \(G=(V,E)\), \(V=\{1,2,\ldots ,n\}\), be a simple connected graph with \(n\ge 3\) vertices and m edges, with vertex degree sequence \(d_1\ge d_2\ge \cdots \ge d_n\), \(d_i=d(i)\). The augmented Zagreb index is defined as \(AZI=\sum _{i\sim j}\left( \frac{d_i d_j}{d_i+d_j-2}\right) ^3\), where \(i\sim j\) denotes adjacency of vertices i and j. Some new lower bounds for AZI are obtained.

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Acknowledgements

This paper was supported by Serbian Ministry of Education, Science and Technological Development through Grant Nos. 174033, TR32009 and TR3212.

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Authors and Affiliations

  1. Faculty of Science, University of Kragujevac, P. O. Box 60, Kragujevac, 34000, Serbia

    Boris Furtula & Ivan Gutman

  2. Faculty of Electronics Engineering, University of Niš, A. Medvedeva 14, Niš, 18000, Serbia

    Marjan Matejić, Emina Milovanović & Igor Milovanović

Authors
  1. Boris Furtula
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  2. Ivan Gutman
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  3. Marjan Matejić
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  4. Emina Milovanović
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  5. Igor Milovanović
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Correspondence to Boris Furtula.

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Furtula, B., Gutman, I., Matejić, M. et al. Some new lower bounds for augmented Zagreb index. J. Appl. Math. Comput. 61, 405–415 (2019). https://doi.org/10.1007/s12190-019-01258-x

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  • DOI: https://doi.org/10.1007/s12190-019-01258-x

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