IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i20p4256-d1257932.html
   My bibliography  Save this article

Ad-Hoc Lanzhou Index

Author

Listed:
  • Akbar Ali

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il P.O. Box 2240, Saudi Arabia)

  • Yilun Shang

    (Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK)

  • Darko Dimitrov

    (Faculty of Information Studies, 8000 Novo Mesto, Slovenia)

  • Tamás Réti

    (Donát Bánki Faculty of Mechanical and Safety Engineering, Óbuda University, H-1034 Budapest, Hungary)

Abstract

This paper initiates the study of the mathematical aspects of the ad-hoc Lanzhou index. If G is a graph with the vertex set { x 1 , … , x n } , then the ad-hoc Lanzhou index of G is defined by L z ˜ ( G ) = ∑ i = 1 n d i ( n − 1 − d i ) 2 , where d i represents the degree of the vertex x i . Several identities for the ad-hoc Lanzhou index, involving some existing topological indices, are established. The problems of finding graphs with the extremum values of the ad-hoc Lanzhou index from the following sets of graphs are also attacked: (i) the set of all connected ξ -cyclic graphs of a fixed order, (ii) the set of all connected molecular ξ -cyclic graphs of a fixed order, (iii) the set of all graphs of a fixed order, and (iv) the set of all connected molecular graphs of a fixed order.

Suggested Citation

  • Akbar Ali & Yilun Shang & Darko Dimitrov & Tamás Réti, 2023. "Ad-Hoc Lanzhou Index," Mathematics, MDPI, vol. 11(20), pages 1-19, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4256-:d:1257932
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/20/4256/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/20/4256/
    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:11:y:2023:i:20:p:4256-:d:1257932. 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.