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On the maximum ABC index of graphs without pendent vertices

Author

Listed:
  • Shao, Zehui
  • Wu, Pu
  • Gao, Yingying
  • Gutman, Ivan
  • Zhang, Xiujun

Abstract

Let G be a simple graph. The atom–bond connectivity index (ABC) of G is defined as ABC(G)=∑uv∈E(G)d(u)+d(v)−2d(u)d(v), where d(v) denotes the degree of vertex v of G. We characterize the graphs with n vertices, minimum vertex degree ≥ 2, and m edges for m=2n−4 and m=2n−3, that have maximum ABC index.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:315:y:2017:i:c:p:298-312
    DOI: 10.1016/j.amc.2017.07.075
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    References listed on IDEAS

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    1. Dimitrov, Darko & Du, Zhibin & da Fonseca, Carlos M., 2016. "On structural properties of trees with minimal atom-bond connectivity index III: Trees with pendent paths of length three," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 276-290.
    2. Gao, Wei & Farahani, Mohammad Reza & Wang, Shaohui & Husin, Mohamad Nazri, 2017. "On the edge-version atom-bond connectivity and geometric arithmetic indices of certain graph operations," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 11-17.
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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.
    2. Shaohui Wang & Zehui Shao & Jia-Bao Liu & Bing Wei, 2019. "The Bounds of Vertex Padmakar–Ivan Index on k -Trees," Mathematics, MDPI, vol. 7(4), pages 1-10, April.
    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. Muhammad Imran & Muhammad Kamran Siddiqui & Amna A. E. Abunamous & Dana Adi & Saida Hafsa Rafique & Abdul Qudair Baig, 2018. "Eccentricity Based Topological Indices of an Oxide Network," Mathematics, MDPI, vol. 6(7), pages 1-13, July.
    5. 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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