IDEAS home Printed from https://ideas.repec.org/a/hin/jjmath/3795448.html
   My bibliography  Save this article

Algorithmic Complexity and Bounds for Domination Subdivision Numbers of Graphs

Author

Listed:
  • Fu-Tao Hu
  • Chang-Xu Zhang
  • Shu-Cheng Yang
  • Xiaogang Liu

Abstract

Let G=V,E be a simple graph. A subset D⊆V is a dominating set if every vertex not in D is adjacent to a vertex in D. The domination number of G, denoted by γG, is the smallest cardinality of a dominating set of G. The domination subdivision number sdγG of G is the minimum number of edges that must be subdivided (each edge can be subdivided at most once) in order to increase the domination number. In 2000, Haynes et al. showed that sdγG≤dGv+dGv−1 for any edge uv∈EG with dGu≥2 and dGv≥2 where G is a connected graph with order no less than 3. In this paper, we improve the above bound to sdγG≤dGu+dGv−NGu∩NGv−1, and furthermore, we show the decision problem for determining whether sdγG=1 is NP-hard. Moreover, we show some bounds or exact values for domination subdivision numbers of some graphs.

Suggested Citation

  • Fu-Tao Hu & Chang-Xu Zhang & Shu-Cheng Yang & Xiaogang Liu, 2024. "Algorithmic Complexity and Bounds for Domination Subdivision Numbers of Graphs," Journal of Mathematics, Hindawi, vol. 2024, pages 1-10, February.
    • Handle: RePEc:hin:jjmath:3795448
    DOI: 10.1155/2024/3795448
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/jmath/2024/3795448.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/jmath/2024/3795448.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2024/3795448?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
    ---><---

    More about this item

    Statistics

    Access and download statistics

    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:hin:jjmath:3795448. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.