IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i4p312-d217855.html
   My bibliography  Save this article

Linear Operators That Preserve the Genus of a Graph

Author

Listed:
  • LeRoy B. Beasley

    (Department of Mathematics and Statistics, Utah State University, Logan, UT 84322-3900, USA)

  • Jeong Han Kim

    (School of Computational Sciences, Korean Institute for Advanced Study, Seoul 02455, Korea)

  • Seok-Zun Song

    (Department of Mathematics, Jeju National University, Jeju 63243, Korea)

Abstract

A graph has genus k if it can be embedded without edge crossings on a smooth orientable surface of genus k and not on one of genus k − 1 . A mapping of the set of graphs on n vertices to itself is called a linear operator if the image of a union of graphs is the union of their images and if it maps the edgeless graph to the edgeless graph. We investigate linear operators on the set of graphs on n vertices that map graphs of genus k to graphs of genus k and graphs of genus k + 1 to graphs of genus k + 1 . We show that such linear operators are necessarily vertex permutations. Similar results with different restrictions on the genus k preserving operators give the same conclusion.

Suggested Citation

  • LeRoy B. Beasley & Jeong Han Kim & Seok-Zun Song, 2019. "Linear Operators That Preserve the Genus of a Graph," Mathematics, MDPI, vol. 7(4), pages 1-6, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:312-:d:217855
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/4/312/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/4/312/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:7:y:2019:i:4:p:312-:d:217855. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.