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A solution of the conjecture about big vertices of minimal-ABC trees

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  • Dimitrov, Darko
  • Du, Zhibin

Abstract

The problem of full determination of trees with a minimal value of the ABC index is very hard and famous in mathematical chemistry. A well-known conjecture is that the big vertices (vertices of degree larger than 2, which are not adjacent to a vertex of degree 2) of a tree with a minimal value of the ABC index induce a star graph. Here we give an affirmative answer to this conjecture and thus make a significant step towards the complete characterization of trees with minimal ABC index.

Suggested Citation

  • Dimitrov, Darko & Du, Zhibin, 2021. "A solution of the conjecture about big vertices of minimal-ABC trees," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    • Handle: RePEc:eee:apmaco:v:397:y:2021:i:c:s0096300320307712
    DOI: 10.1016/j.amc.2020.125818
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    References listed on IDEAS

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    1. Dimitrov, Darko, 2017. "On structural properties of trees with minimal atom-bond connectivity index IV: Solving a conjecture about the pendent paths of length three," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 418-430.
    2. 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.
    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.
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    Cited by:

    1. Du, Jianwei & Sun, Xiaoling, 2024. "On bond incident degree index of chemical trees with a fixed order and a fixed number of leaves," Applied Mathematics and Computation, Elsevier, vol. 464(C).

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