IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v309y2017icp85-92.html
   My bibliography  Save this article

On extremal cacti with respect to the Szeged index

Author

Listed:
  • Wang, Shujing

Abstract

The Szeged index of a graph G is defined as Sz(G)=∑e=uv∈Enu(e)nv(e), where nu(e) and nv(e) are, respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u. A cactus is a graph in which any two cycles have at most one common vertex. Let C(n,k) denote the class of all cacti with order n and k cycles, and Cnt denote the class of all cacti with order n and t pendant vertices. In this paper, a lower bound of the Szeged index for cacti of order n with k cycles is determined, and all the graphs that achieve the lower bound are identified. As well, the unique graph in Cnt with minimum Szeged index is characterized.

Suggested Citation

  • Wang, Shujing, 2017. "On extremal cacti with respect to the Szeged index," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 85-92.
    • Handle: RePEc:eee:apmaco:v:309:y:2017:i:c:p:85-92
    DOI: 10.1016/j.amc.2017.03.036
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317302205
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.03.036?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. Lei, Hui & Yang, Hua, 2015. "Bounds for the Sum-Balaban index and (revised) Szeged index of regular graphs," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1259-1266.
    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. Hechao Liu & Hanyuan Deng & Zikai Tang, 2019. "Minimum Szeged index among unicyclic graphs with perfect matchings," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 443-455, August.
    2. Ji, Shengjin & Liu, Mengmeng & Wu, Jianliang, 2018. "A lower bound of revised Szeged index of bicyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 480-487.
    3. Wang, Guangfu & Li, Shuchao & Qi, Dongchao & Zhang, Huihui, 2018. "On the edge-Szeged index of unicyclic graphs with given diameter," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 94-106.

    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. Ji, Shengjin & Liu, Mengmeng & Wu, Jianliang, 2018. "A lower bound of revised Szeged index of bicyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 480-487.
    2. Črepnjak, Matevž & Tratnik, Niko, 2017. "The Szeged index and the Wiener index of partial cubes with applications to chemical graphs," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 324-333.
    3. Knor, Martin & Kranjc, Jaka & Škrekovski, Riste & Tepeh, Aleksandra, 2017. "On the minimum value of sum-Balaban index," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 203-210.

    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:309:y:2017:i:c:p:85-92. 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.