IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v416y2022ics0096300321008377.html
   My bibliography  Save this article

The Wiener index of signed graphs

Author

Listed:
  • Spiro, Sam

Abstract

The Wiener index of a graph W(G) is a well studied topological index for graphs. An outstanding problem of Šoltés is to find graphs G such that W(G)=W(G−v) for all vertices v∈V(G), with the only known example being G=C11. We relax this problem by defining a notion of Wiener indices for signed graphs, which we denote by Wσ(G), and under this relaxation we construct many signed graphs such that Wσ(G)=Wσ(G−v) for all v∈V(G). This ends up being related to a problem of independent interest, which asks when it is possible to 2-color the edges of a graph G such that there is a path between any two vertices of G which uses each color the same number of times. We briefly explore this latter problem, as well as its natural extension to r-colorings.

Suggested Citation

  • Spiro, Sam, 2022. "The Wiener index of signed graphs," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    • Handle: RePEc:eee:apmaco:v:416:y:2022:i:c:s0096300321008377
    DOI: 10.1016/j.amc.2021.126755
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321008377
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126755?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. Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2016. "Some remarks on Wiener index of oriented graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 631-636.
    2. Knor, Martin & Majstorović, Snježana & Škrekovski, Riste, 2018. "Graphs preserving Wiener index upon vertex removal," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 25-32.
    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. Sun, Daoqiang & Li, Long & Liu, Kai & Wang, Hua & Yang, Yu, 2022. "Enumeration of subtrees of planar two-tree networks," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    2. Guo, Songlin & Wang, Wei & Wang, Chuanming, 2023. "Disproof of a conjecture on the minimum Wiener index of signed trees," Applied Mathematics and Computation, Elsevier, vol. 439(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. Knor, Martin & Majstorović, Snježana & Škrekovski, Riste, 2018. "Graphs preserving Wiener index upon vertex removal," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 25-32.
    2. Andova, Vesna & Orlić, Damir & Škrekovski, Riste, 2017. "Leapfrog fullerenes and Wiener index," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 281-288.
    3. Hriňáková, Katarína & Knor, Martin & Škrekovski, Riste, 2019. "An inequality between variable wiener index and variable szeged index," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    4. Wang, Guangfu & Liu, Yajing, 2020. "The edge-Wiener index of zigzag nanotubes," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    5. Al-Yakoob, Salem & Stevanović, Dragan, 2020. "On transmission irregular starlike trees," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    6. Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2016. "Digraphs with large maximum Wiener index," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 260-267.

    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:apmaco:v:416:y:2022:i:c:s0096300321008377. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.