IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v40y2020i4d10.1007_s10878-020-00655-4.html
   My bibliography  Save this article

The maximum Wiener index of maximal planar graphs

Author

Listed:
  • Debarun Ghosh

    (Central European University)

  • Ervin Győri

    (Central European University
    Alfréd Rényi Institute of Mathematics)

  • Addisu Paulos

    (Central European University
    Addis Ababa University)

  • Nika Salia

    (Central European University
    Alfréd Rényi Institute of Mathematics)

  • Oscar Zamora

    (Central European University
    Universidad de Costa Rica)

Abstract

The Wiener index of a connected graph is the sum of the distances between all pairs of vertices in the graph. It was conjectured that the Wiener index of an n-vertex maximal planar graph is at most $$\lfloor \frac{1}{18}(n^3+3n^2)\rfloor $$ ⌊ 1 18 ( n 3 + 3 n 2 ) ⌋ . We prove this conjecture and determine the unique n-vertex maximal planar graph attaining this maximum, for every $$ n\ge 10$$ n ≥ 10 .

Suggested Citation

  • Debarun Ghosh & Ervin Győri & Addisu Paulos & Nika Salia & Oscar Zamora, 2020. "The maximum Wiener index of maximal planar graphs," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 1121-1135, November.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:4:d:10.1007_s10878-020-00655-4
    DOI: 10.1007/s10878-020-00655-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-020-00655-4
    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/s10878-020-00655-4?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. Kinkar Ch. Das & M. J. Nadjafi-Arani, 2017. "On maximum Wiener index of trees and graphs with given radius," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 574-587, August.
    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. Xiangxiang Liu & Ligong Wang & Xihe Li, 2020. "The Wiener index of hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 39(2), pages 351-364, February.
    2. Hongfang Liu & Jinxia Liang & Yuhu Liu & Kinkar Chandra Das, 2023. "A Combinatorial Approach to Study the Nordhaus–Guddum-Type Results for Steiner Degree Distance," Mathematics, MDPI, vol. 11(3), pages 1-19, February.
    3. Kexiang Xu & Haiqiong Liu & Kinkar Ch. Das & Sandi Klavžar, 2018. "Embeddings into almost self-centered graphs of given radius," Journal of Combinatorial Optimization, Springer, vol. 36(4), pages 1388-1410, November.
    4. Hamid Darabi & Yaser Alizadeh & Sandi Klavžar & Kinkar Chandra Das, 2021. "On the relation between Wiener index and eccentricity of a graph," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 817-829, May.

    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_s10878-020-00655-4. 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.