IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v425y2022ics009630032200159x.html
   My bibliography  Save this article

Toughness and normalized Laplacian eigenvalues of graphs

Author

Listed:
  • Huang, Xueyi
  • Das, Kinkar Chandra
  • Zhu, Shunlai

Abstract

Given a connected graph G, the toughness τG is defined as the minimum value of the ratio |S|/ωG−S, where S ranges over all vertex cut sets of G, and ωG−S is the number of connected components in the subgraph G−S obtained by deleting all vertices of S from G. In this paper, we provide a lower bound for the toughness τG in terms of the maximum degree, minimum degree and normalized Laplacian eigenvalues of G. This can be viewed as a slight generalization of Brouwer’s toughness conjecture, which was confirmed by Gu (2021). Furthermore, we give a characterization of those graphs attaining the two lower bounds regarding toughness and Laplacian eigenvalues provided by Gu and Haemers (2022).

Suggested Citation

  • Huang, Xueyi & Das, Kinkar Chandra & Zhu, Shunlai, 2022. "Toughness and normalized Laplacian eigenvalues of graphs," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    • Handle: RePEc:eee:apmaco:v:425:y:2022:i:c:s009630032200159x
    DOI: 10.1016/j.amc.2022.127075
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630032200159X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127075?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.

    Citations

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


    Cited by:

    1. Ganie, Hilal A. & Rather, Bilal Ahmad & Das, Kinkar Chandra, 2023. "On the normalized distance laplacian eigenvalues of graphs," Applied Mathematics and Computation, Elsevier, vol. 438(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:eee:apmaco:v:425:y:2022:i:c:s009630032200159x. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.