IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/vyid10.1007_s10878-020-00596-y.html
   My bibliography  Save this article

The complexity of total edge domination and some related results on trees

Author

Listed:
  • Zhuo Pan

    (Lanzhou University)

  • Yu Yang

    (Lanzhou University)

  • Xianyue Li

    (Lanzhou University)

  • Shou-Jun Xu

    (Lanzhou University)

Abstract

For a graph $$G = (V, E)$$G=(V,E) with vertex set V and edge set E, a subset F of E is called an edge dominating set (resp. a total edge dominating set) if every edge in $$E\backslash F$$E\F (resp. in E) is adjacent to at least one edge in F, the minimum cardinality of an edge dominating set (resp. a total edge dominating set) of G is the edge domination number (resp. total edge domination number) of G, denoted by $$\gamma ^{\prime }(G)$$γ′(G) (resp. $$\gamma _t^{\prime }(G)$$γt′(G)). In the present paper, we first prove that the total edge domination problem is NP-complete for bipartite graphs with maximum degree 3. Then, for a graph G, we give the inequality $$\gamma ^{\prime }(G)\leqslant \gamma ^{\prime }_{t}(G)\leqslant 2\gamma ^{\prime }(G)$$γ′(G)⩽γt′(G)⩽2γ′(G) and characterize the trees T which obtain the upper or lower bounds in the inequality.

Suggested Citation

  • Zhuo Pan & Yu Yang & Xianyue Li & Shou-Jun Xu, 0. "The complexity of total edge domination and some related results on trees," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-19.
    • Handle: RePEc:spr:jcomop:v::y::i::d:10.1007_s10878-020-00596-y
    DOI: 10.1007/s10878-020-00596-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-020-00596-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-020-00596-y?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. Zhuo Pan & Xianyue Li & Shou-Jun Xu, 2020. "Complexity and characterization aspects of edge-related domination for graphs," Journal of Combinatorial Optimization, Springer, vol. 40(3), pages 757-773, October.
    2. Zhuo Pan & Xianyue Li & Shou-Jun Xu, 0. "Complexity and characterization aspects of edge-related domination for graphs," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-17.

    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:spr:jcomop:v::y::i::d:10.1007_s10878-020-00596-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.