IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v48y2024i1d10.1007_s10878-024-01195-x.html
   My bibliography  Save this article

First zagreb spectral radius of unicyclic graphs and trees

Author

Listed:
  • Parikshit Das

    (National Institute of Technology Durgapur)

  • Kinkar Chandra Das

    (Sungkyunkwan University)

  • Sourav Mondal

    (Sungkyunkwan University
    SRM Institute of Science and Technology)

  • Anita Pal

    (National Institute of Technology Durgapur)

Abstract

In light of the successful investigation of the adjacency matrix, a significant amount of its modification is observed employing numerous topological indices. The matrix corresponding to the well-known first Zagreb index is one of them. The entries of the first Zagreb matrix are $$d_{u_i}+d_{u_j}$$ d u i + d u j , if $$u_i$$ u i is connected to $$u_j$$ u j ; 0, otherwise, where $$d_{u_i}$$ d u i is degree of i-th vertex. The current work is concerned with the mathematical properties and chemical significance of the spectral radius ( $$\rho _1$$ ρ 1 ) associated with this matrix. The lower and upper bounds of $$\rho _1$$ ρ 1 are computed with characterizing extremal graphs for the class of unicyclic graphs and trees. The chemical connection of the first Zagreb spectral radius is established by exploring its role as a structural descriptor of molecules. The isomer discrimination ability of $$\rho _1$$ ρ 1 is also explained.

Suggested Citation

  • Parikshit Das & Kinkar Chandra Das & Sourav Mondal & Anita Pal, 2024. "First zagreb spectral radius of unicyclic graphs and trees," Journal of Combinatorial Optimization, Springer, vol. 48(1), pages 1-24, August.
    • Handle: RePEc:spr:jcomop:v:48:y:2024:i:1:d:10.1007_s10878-024-01195-x
    DOI: 10.1007/s10878-024-01195-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-024-01195-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-024-01195-x?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bo Deng & Caibing Chang & Kinkar Chandra Das, 2023. "RETRACTED ARTICLE: The Sachs theorem and its application on extended adjacency matrix of graphs," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-12, January.
    2. Tomáš Vetrík & Selvaraj Balachandran, 2020. "General multiplicative Zagreb indices of trees and unicyclic graphs with given matching number," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 953-973, November.
    3. Zheng, Ruiling & Su, Peifeng & Jin, Xian’an, 2023. "Arithmetic-geometric matrix of graphs and its applications," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    4. Huan He & Miaolin Ye & Huan Xu & Guidong Yu, 2023. "RETRACTED ARTICLE: On $${A_{\alpha }}$$ A α -spectrum of a unicyclic graph," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-16, January.
    5. Seyed Mahmoud Sheikholeslami & Akbar Jahanbani & Rana Khoeilar, 2021. "New Results on Zagreb Energy of Graphs," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-6, May.
    6. Roberto Cruz & Juan Daniel Monsalve & Juan Rada, 2021. "The balanced double star has maximum exponential second Zagreb index," Journal of Combinatorial Optimization, Springer, vol. 41(2), pages 544-552, February.
    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.
    1. Gao, Wei & Gao, Yubin, 2024. "The extremal trees for exponential vertex-degree-based topological indices," Applied Mathematics and Computation, Elsevier, vol. 472(C).

    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:spr:jcomop:v:48:y:2024:i:1:d:10.1007_s10878-024-01195-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.