IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v426y2022ics0096300322001916.html
   My bibliography  Save this article

Maximal and maximum dissociation sets in general and triangle-free graphs

Author

Listed:
  • Tu, Jianhua
  • Li, Yuxin
  • Du, Junfeng

Abstract

In a graph G, a subset of vertices is a dissociation set if it induces a subgraph with maximum degree at most 1. A maximal dissociation set of G is a dissociation set which is not a proper subset of any other dissociation sets. A maximum dissociation set is a dissociation set of maximum size. We show that every graph of order n has at most 10n5 maximal dissociation sets, and that every triangle-free graph of order n has at most 6n4 maximal dissociation sets. We also characterize the extremal graphs on which these upper bounds are attained.

Suggested Citation

  • Tu, Jianhua & Li, Yuxin & Du, Junfeng, 2022. "Maximal and maximum dissociation sets in general and triangle-free graphs," Applied Mathematics and Computation, Elsevier, vol. 426(C).
    • Handle: RePEc:eee:apmaco:v:426:y:2022:i:c:s0096300322001916
    DOI: 10.1016/j.amc.2022.127107
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322001916
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127107?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. Das, Joyentanuj & Mohanty, Sumit, 2024. "Maximization of the spectral radius of block graphs with a given dissociation number," Applied Mathematics and Computation, Elsevier, vol. 465(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:426:y:2022:i:c:s0096300322001916. 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.