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On the maximal general ABC index of graphs with given maximum degree

Author

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  • Das, Kinkar Chandra
  • Rodríguez, José M.
  • Sigarreta, José M.

Abstract

The atom-bond connectivity index ABC is a topological index that has recently found remarkable applications in the study of the strain energy of cycloalkanes as well as in rationalizing the stability of linear and branched alkanes. In order to improve the correlation properties of the atom-bond connectivity index for the heat of formation of alkanes, Furtula et al. considered a generalization of this index, namely,ABCα=ABCα(G)=∑uv∈E(G)(du+dv−2dudv)αforanyα∈R∖{0},where dv is the degree of the vertex v and uv denotes the edge connecting the vertices u and v of graph G. Here, we obtain some optimization results for ABCα of the connected graph G.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304872
    DOI: 10.1016/j.amc.2020.125531
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    References listed on IDEAS

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    1. 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.
    2. Shao, Zehui & Wu, Pu & Gao, Yingying & Gutman, Ivan & Zhang, Xiujun, 2017. "On the maximum ABC index of graphs without pendent vertices," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 298-312.
    3. Wu, Xiaoxia & Zhang, Lianzhu, 2019. "On structural properties of ABC-minimal chemical trees," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
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    Cited by:

    1. Paul Bosch & Edil D. Molina & José M. Rodríguez & José M. Sigarreta, 2021. "Inequalities on the Generalized ABC Index," Mathematics, MDPI, vol. 9(10), pages 1-17, May.

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