IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v14y2026i2p321-d1842990.html

Sharp Bounds on the Spectral Radius and Energy of Arithmetic–Geometric Matrix

Author

Listed:
  • Hilal A. Ganie

    (Department of Mathematics, Government Degree College Uri, Srinagar 193123, Kashmir, India)

  • Amal Alsaluli

    (Department of Mathematics, College of Science, University of Bisha, Bisha 61922, Saudi Arabia)

Abstract

Let Z be a graph of order n with m edges. Let A a g ( Z ) represents the arithmetic–geometric matrix of Z . The eigenvalues of the matrix A a g ( Z ) are called the arithmetic–geometric eigenvalues, and the eigenvalue with the largest modulus is called the arithmetic–geometric spectral radius of Z . The sum of the absolute values of the arithmetic–geometric eigenvalues is called the arithmetic–geometric energy of Z . In this paper, we establish sharp upper and lower bounds for the AM-GM spectral radius in terms of various graph parameters and provide a complete characterization of the extremal graphs that attain these bounds. Additionally, we derive new bounds for the AM-GM energy of a graph and identify the corresponding extremal structures. In both contexts, our results significantly improve upon several existing bounds reported in the literature.

Suggested Citation

  • Hilal A. Ganie & Amal Alsaluli, 2026. "Sharp Bounds on the Spectral Radius and Energy of Arithmetic–Geometric Matrix," Mathematics, MDPI, vol. 14(2), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:2:p:321-:d:1842990
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/14/2/321/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/14/2/321/
    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:14:y:2026:i:2:p:321-:d:1842990. 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.