IDEAS home Printed from https://ideas.repec.org/a/wly/jjmath/v2022y2022i1n7783128.html

On the Maximum Symmetric Division Deg Index of k‐Cyclic Graphs

Author

Listed:
  • Abeer M. Albalahi
  • Akbar Ali

Abstract

Let G be a graph. Denote by du, the degree of a vertex u of G and represent by vw, the edge of G with the end‐vertices v and w. The sum of the quantities du2+dv2du−1dv−1 over all edges uv of G is known as the symmetric division deg (SDD) index of G. A connected graph with n vertices and n − 1 + k edges is known as a (connected)k‐cyclic graph. One of the results proved in this study is that the graph possessing the largest SDD index over the class of all connectedk‐cyclic graphs of a fixed order n must have the maximum degree n − 1. By utilizing this result, the graphs attaining the largest SDD index over the aforementioned class of graphs are determined for every k = 0,1, …, 5. Although, the deduced results, for k = 0,1,2, are already known, however, they are proved here in a shorter and an alternative way. Also, the deduced results, for k = 3,4,5, are new, and they provide answers to two open questions posed in the literature.

Suggested Citation

  • Abeer M. Albalahi & Akbar Ali, 2022. "On the Maximum Symmetric Division Deg Index of k‐Cyclic Graphs," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:7783128
    DOI: 10.1155/2022/7783128
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2022/7783128
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2022/7783128?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Bin Yang & Vinayak V. Manjalapur & Sharanu P. Sajjan & Madhura M. Mathai & Jia-Bao Liu, 2019. "On Extended Adjacency Index with Respect to Acyclic, Unicyclic and Bicyclic Graphs," Mathematics, MDPI, vol. 7(7), pages 1-9, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      More about this item

      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:wly:jjmath:v:2022:y:2022:i:1:n:7783128. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/1469 .

      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.