IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i3p437-d1578858.html
   My bibliography  Save this article

An Upper Bound for the Eternal Roman Domination Number

Author

Listed:
  • Richard Brewster

    (Department of Mathematics and Statistics, Thompson Rivers University, Kamloops, BC V2C 0C8, Canada)

  • Gary MacGillivray

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 2Y2, Canada)

  • Ethan Williams

    (Institute of Discrete Mathematics, Graz University of Technology, 8010 Graz, Austria)

Abstract

Imagine using mobile guards to defend the vertices of a graph G from a sequence of attacks subject to the conditions that after each attack: (i) each guard either remains in place or moves to an adjacent vertex; (ii) the configuration of guards forms a Roman-dominating set; and (iii) there is at least one guard on each attacked vertex. We show that it is always possible to defend the vertices of a tree with n vertices using at most 5 n 6 guards and that this bound is tight.

Suggested Citation

  • Richard Brewster & Gary MacGillivray & Ethan Williams, 2025. "An Upper Bound for the Eternal Roman Domination Number," Mathematics, MDPI, vol. 13(3), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:437-:d:1578858
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/3/437/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/3/437/
    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:437-:d:1578858. 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.