IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v157y2022ics0960077922001357.html
   My bibliography  Save this article

On total irregularity index of trees with given number of segments or branching vertices

Author

Listed:
  • Yousaf, Shamaila
  • Bhatti, Akhlaq Ahmad
  • Ali, Akbar

Abstract

A non-negative graph invariant IM is said to be an irregularity measure of a graph G if the following condition holds: IM(G)=0 if and only if G is regular. There exist many irregularity measures in the literature and the Albertson index is probably the most studied such measure. In order to overcome several drawbacks of the Albertson index, a variant of the Albertson index was recently introduced under the name ǣtotal irregularityǥ. The total irregularity index of a graph G is defined as 12∑u,w∈V(G)|degG(u)−degG(w)|, where degG(w) is the degree of a vertex w∈V(G). By an n-vertex tree, we mean a tree of order n. In the present study, the best possible sharp upper and lower bounds on the total irregularity index of n-vertex trees with fixed number of segments or branching vertices are derived.

Suggested Citation

  • Yousaf, Shamaila & Bhatti, Akhlaq Ahmad & Ali, Akbar, 2022. "On total irregularity index of trees with given number of segments or branching vertices," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001357
    DOI: 10.1016/j.chaos.2022.111925
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922001357
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.111925?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. Slim Belhaiza & Nair Maria Maia Abreu & Pierre Hansen & Carla Silva Oliveira, 2005. "Variable Neighborhood Search for Extremal Graphs. XI. Bounds on Algebraic Connectivity," Springer Books, in: David Avis & Alain Hertz & Odile Marcotte (ed.), Graph Theory and Combinatorial Optimization, chapter 0, pages 1-16, Springer.
    2. Lihua You & Jieshan Yang & Yingxue Zhu & Zhifu You, 2014. "The Maximal Total Irregularity of Bicyclic Graphs," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Raza, Zahid & Akhter, Shehnaz, 2023. "On maximum Zagreb connection indices for trees with fixed domination number," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

    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. Ashrafi, Ali Reza & Ghalavand, Ali, 2020. "Note on non-regular graphs with minimal total irregularity," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    2. Asad Khan & Ghulam Haidar & Naeem Abbas & Murad Ul Islam Khan & Azmat Ullah Khan Niazi & Asad Ul Islam Khan, 2023. "Metric Dimensions of Bicyclic Graphs," Mathematics, MDPI, vol. 11(4), pages 1-17, February.

    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:eee:chsofr:v:157:y:2022:i:c:s0960077922001357. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.