IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v40y2020i4d10.1007_s10878-020-00643-8.html
   My bibliography  Save this article

General multiplicative Zagreb indices of trees and unicyclic graphs with given matching number

Author

Listed:
  • Tomáš Vetrík

    (University of the Free State)

  • Selvaraj Balachandran

    (University of the Free State
    SASTRA Deemed University)

Abstract

The first general multiplicative Zagreb index of a graph G is defined as $$P_1^a (G) = \prod _{v \in V(G)} (deg_G (v))^a$$ P 1 a ( G ) = ∏ v ∈ V ( G ) ( d e g G ( v ) ) a and the second general multiplicative Zagreb index is $$P_2^a (G) = \prod _{v \in V(G)} (deg_G (v))^{a \, deg_G (v)}$$ P 2 a ( G ) = ∏ v ∈ V ( G ) ( d e g G ( v ) ) a d e g G ( v ) , where V(G) is the vertex set of G, $$deg_{G} (v)$$ d e g G ( v ) is the degree of v in G and $$a \ne 0$$ a ≠ 0 is a real number. We present lower and upper bounds on the general multiplicative Zagreb indices for trees and unicyclic graphs of given order with a perfect matching. We also obtain lower and upper bounds for trees and unicyclic graphs of given order and matching number. All the trees and unicyclic graphs which achieve the bounds are presented, thus our bounds are sharp. Bounds for the classical multiplicative Zagreb indices are special cases of our theorems and those bounds are new results as well.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:4:d:10.1007_s10878-020-00643-8
    DOI: 10.1007/s10878-020-00643-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-020-00643-8
    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/s10878-020-00643-8?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. Wang, Shaohui & Wang, Chunxiang & Liu, Jia-Bao, 2018. "On extremal multiplicative Zagreb indices of trees with given domination number," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 338-350.
    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. Ayu Ameliatul Shahilah Ahmad Jamri & Fateme Movahedi & Roslan Hasni & Rudrusamy Gobithaasan & Mohammad Hadi Akhbari, 2022. "Minimum Randić Index of Trees with Fixed Total Domination Number," Mathematics, MDPI, vol. 10(20), pages 1-13, October.
    2. Fang Gao & Xiaoxin Li & Kai Zhou & Jia-Bao Liu, 2018. "The Extremal Graphs of Some Topological Indices with Given Vertex k -Partiteness," Mathematics, MDPI, vol. 6(11), pages 1-11, November.
    3. Shaohui Wang & Zehui Shao & Jia-Bao Liu & Bing Wei, 2019. "The Bounds of Vertex Padmakar–Ivan Index on k -Trees," Mathematics, MDPI, vol. 7(4), pages 1-10, April.
    4. Shaohui Wang & Chunxiang Wang & Lin Chen & Jia-Bao Liu & Zehui Shao, 2018. "Maximizing and Minimizing Multiplicative Zagreb Indices of Graphs Subject to Given Number of Cut Edges," Mathematics, MDPI, vol. 6(11), pages 1-10, October.

    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:40:y:2020:i:4:d:10.1007_s10878-020-00643-8. 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.