IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v13y2007i1d10.1007_s10878-006-9014-8.html
   My bibliography  Save this article

Graphs with large paired-domination number

Author

Listed:
  • Michael A. Henning

    (University of KwaZulu-Natal)

Abstract

In this paper, we continue the study of paired-domination in graphs introduced by Haynes and Slater (1998) Networks 32: 199–206. A paired-dominating set of a graph G with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of G, denoted by $$\gamma_{\rm pr}(G)$$ , is the minimum cardinality of a paired-dominating set of G. Let G be a connected graph of order n with minimum degree at least two. Haynes and Slater (1998) Networks 32: 199–206, showed that if n ≥ 6, then $$\gamma_{\rm pr}(G) \le 2n/3$$ . In this paper, we show that there are exactly ten graphs that achieve equality in this bound. For n ≥ 14, we show that $$\gamma_{\rm pr}(G) \le 2(n-1)/3$$ and we characterize the (infinite family of) graphs that achieve equality in this bound.

Suggested Citation

  • Michael A. Henning, 2007. "Graphs with large paired-domination number," Journal of Combinatorial Optimization, Springer, vol. 13(1), pages 61-78, January.
    • Handle: RePEc:spr:jcomop:v:13:y:2007:i:1:d:10.1007_s10878-006-9014-8
    DOI: 10.1007/s10878-006-9014-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-006-9014-8
    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/s10878-006-9014-8?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. Michael A. Henning & Michael D. Plummer, 2005. "Vertices Contained in all or in no Minimum Paired-Dominating Set of a Tree," Journal of Combinatorial Optimization, Springer, vol. 10(3), pages 283-294, November.
    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. Lei Chen & Changhong Lu & Zhenbing Zeng, 2012. "Vertices in all minimum paired-dominating sets of block graphs," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 176-191, October.
    2. Henning, Michael A. & Pilśniak, Monika & Tumidajewicz, Elżbieta, 2022. "Bounds on the paired domination number of graphs with minimum degree at least three," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    3. Michael A. Henning & John McCoy, 2011. "Which trees have a differentiating-paired dominating set?," Journal of Combinatorial Optimization, Springer, vol. 22(1), pages 1-18, July.
    4. Justin Southey & Michael A. Henning, 2011. "A characterization of graphs with disjoint dominating and paired-dominating sets," Journal of Combinatorial Optimization, Springer, vol. 22(2), pages 217-234, August.
    5. Lei Chen & Changhong Lu & Zhenbing Zeng, 2010. "Labelling algorithms for paired-domination problems in block and interval graphs," Journal of Combinatorial Optimization, Springer, vol. 19(4), pages 457-470, May.
    6. Paul Dorbec & Michael A. Henning, 2011. "Upper paired-domination in claw-free graphs," Journal of Combinatorial Optimization, Springer, vol. 22(2), pages 235-251, August.
    7. Wei Yang & Xinhui An & Baoyindureng Wu, 2017. "Paired-domination number of claw-free odd-regular graphs," Journal of Combinatorial Optimization, Springer, vol. 33(4), pages 1266-1275, May.
    8. Teresa W. Haynes & Michael A. Henning, 2021. "Bounds on the semipaired domination number of graphs with minimum degree at least two," Journal of Combinatorial Optimization, Springer, vol. 41(2), pages 451-486, February.
    9. S. L. Fitzpatrick & B. L. Hartnell, 2010. "Well paired-dominated graphs," Journal of Combinatorial Optimization, Springer, vol. 20(2), pages 194-204, August.

    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. Lei Chen & Changhong Lu & Zhenbing Zeng, 2012. "Vertices in all minimum paired-dominating sets of block graphs," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 176-191, October.
    2. Justin Southey & Michael A. Henning, 2011. "A characterization of graphs with disjoint dominating and paired-dominating sets," Journal of Combinatorial Optimization, Springer, vol. 22(2), pages 217-234, August.
    3. Paul Dorbec & Michael A. Henning, 2011. "Upper paired-domination in claw-free graphs," Journal of Combinatorial Optimization, Springer, vol. 22(2), pages 235-251, August.
    4. Michael A. Henning & John McCoy, 2011. "Which trees have a differentiating-paired dominating set?," Journal of Combinatorial Optimization, Springer, vol. 22(1), pages 1-18, July.
    5. Paul Dorbec & Sylvain Gravier & Michael A. Henning, 2007. "Paired-domination in generalized claw-free graphs," Journal of Combinatorial Optimization, Springer, vol. 14(1), pages 1-7, July.

    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:13:y:2007:i:1:d:10.1007_s10878-006-9014-8. 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: 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.