IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i13p2129-d1690511.html
   My bibliography  Save this article

Circulant Digraphs with Larger Linear Guessing Number and Smaller Degree

Author

Listed:
  • Aixian Zhang

    (Department of Mathematical Sciences, Xi’an University of Technology, Xi’an 710048, China)

  • Keqin Feng

    (Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China)

Abstract

The guessing number of a digraph is a new invariant in graph theory raised by S. Riis in 2006 and based on its applications in network coding and boolean circuit complexity theory. In this paper, we present the lower and upper bounds on a guessing number and linear guessing number of circulant digraphs by using cyclic codes. As an application of the lower bound, we construct a series of circulant digraphs with a larger linear guessing number and smaller degree. All of these circulant digraphs provide negative answers to S. Riis’ two open problems on the guessing number proposed in [Proceedings of the 2006 4th International Symposium on Modeling and Optimization in Mobile]. We also give a method to construct circulant digraphs with good estimation on their (linear) guessing number from cyclic codes.

Suggested Citation

  • Aixian Zhang & Keqin Feng, 2025. "Circulant Digraphs with Larger Linear Guessing Number and Smaller Degree," Mathematics, MDPI, vol. 13(13), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2129-:d:1690511
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/13/2129/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/13/2129/
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:gam:jmathe:v:13:y:2025:i:13:p:2129-:d:1690511. 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.