IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v313y2017icp418-430.html
   My bibliography  Save this article

On structural properties of trees with minimal atom-bond connectivity index IV: Solving a conjecture about the pendent paths of length three

Author

Listed:
  • Dimitrov, Darko

Abstract

The atom-bond connectivity (ABC) index is one of the most investigated degree-based molecular structure descriptors with a variety of chemical applications. It is known that among all connected graphs, the trees minimize the ABC index. However, a full characterization of trees with a minimal ABC index is still an open problem. By now, one of the proved properties is that a tree with a minimal ABC index may have, at most, one pendent path of length 3, with the conjecture that it cannot be a case if the order of a tree is larger than 1178. Here, we provide an affirmative answer of a strengthened version of that conjecture, showing that a tree with minimal ABC index cannot contain a pendent path of length 3 if its order is larger than 415.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:apmaco:v:313:y:2017:i:c:p:418-430
    DOI: 10.1016/j.amc.2017.06.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317304265
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2017.06.014?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    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. 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).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:313:y:2017:i:c:p:418-430. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.