IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v282y2016icp276-290.html
   My bibliography  Save this article

On structural properties of trees with minimal atom-bond connectivity index III: Trees with pendent paths of length three

Author

Listed:
  • Dimitrov, Darko
  • Du, Zhibin
  • da Fonseca, Carlos M.

Abstract

The atom-bond connectivity (ABC) index is a degree-based graph topological index that found chemical applications, including those of predicting the stability of alkanes and the strain energy of cycloalkanes. Several structural properties of the trees with minimal ABC index were proved recently, however the complete characterization of the minimal-ABC trees is still an open problem. It is known that minimal-ABC trees can have at most one pendent path of length 3. It is also known that the minimal-ABC trees that have a pendent path of length 3 do not contain so-called Bk-branches, with k ≥ 4, and do not contain more than two B2-branches. Here, we improve the latter result by showing that minimal-ABC trees of order larger than 168 and with a pendent path of length 3 do not contain B2-branches. Moreover, we show that trees with minimal ABC index with a pendent path of length 3 do not contain B1-branches.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:282:y:2016:i:c:p:276-290
    DOI: 10.1016/j.amc.2016.02.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316301229
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.02.019?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.

    Citations

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


    Cited by:

    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, 2021. "A solution of the conjecture about big vertices of minimal-ABC trees," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    3. 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.
    4. 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.

    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:282:y:2016:i:c:p:276-290. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.