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Bounds for the augmented Zagreb and the atom-bond connectivity indices

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  • Palacios, José Luis

Abstract

Using electrical networks and majorization we obtain a lower bound for the augmented Zagreb index in terms of the number of vertices and edges, and the maximum vertex degree. An analogous upper bound for the atom-bond connectivity index is also obtained. These bounds, which are attained by the complete graph Kn, are not comparable to the ones found in the literature.

Suggested Citation

  • Palacios, José Luis, 2017. "Bounds for the augmented Zagreb and the atom-bond connectivity indices," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 141-145.
    • Handle: RePEc:eee:apmaco:v:307:y:2017:i:c:p:141-145
    DOI: 10.1016/j.amc.2017.03.009
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    Cited by:

    1. Sun, Xiaoling & Gao, Yubin & Du, Jianwei & Xu, Lan, 2018. "Augmented Zagreb index of trees and unicyclic graphs with perfect matchings," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 75-81.
    2. Jiang, Yisheng & Lu, Mei, 2021. "Maximal augmented Zagreb index of trees with given diameter," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    3. Lin, Wenshui & Chen, Jianfeng & Wu, Zhixi & Dimitrov, Darko & Huang, Linshan, 2018. "Computer search for large trees with minimal ABC index," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 221-230.
    4. Das, Kinkar Chandra & Rodríguez, José M. & Sigarreta, José M., 2020. "On the maximal general ABC index of graphs with given maximum degree," Applied Mathematics and Computation, Elsevier, vol. 386(C).

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