IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i3p534-d1584677.html
   My bibliography  Save this article

On the Relation Between the Domination Number and Edge Domination Number of Trees and Claw-Free Cubic Graphs

Author

Listed:
  • Zhuo Pan

    (School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China)

  • Peng Pan

    (Gansu Key Laboratory of Applied Mathematics and Complex Systems, School of Mathematics and Statistics, Lanzhou University, Lanzhou 730030, China)

  • Chongshan Tie

    (School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China)

Abstract

For a connected graph G = ( V , E ) , the dominating set in graph G is a subset of vertices F ⊂ V such that every vertex of V − F is adjacent to at least one vertex of F . The minimum cardinality of a dominating set of G , denoted by γ ( G ) , is the domination number of G . The edge dominating set in graph G is a subset of edges S ⊂ E such that every edge of E − S is adjacent to at least one edge of S . The minimum cardinality of an edge dominating set of G , denoted by γ ′ ( G ) , is the edge domination number of G . In this paper, we characterize all trees and claw-free cubic graphs with equal domination and edge domination numbers, respectively.

Suggested Citation

  • Zhuo Pan & Peng Pan & Chongshan Tie, 2025. "On the Relation Between the Domination Number and Edge Domination Number of Trees and Claw-Free Cubic Graphs," Mathematics, MDPI, vol. 13(3), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:534-:d:1584677
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/3/534/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/3/534/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:13:y:2025:i:3:p:534-:d:1584677. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.