IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v6y2018i5p76-d145441.html
   My bibliography  Save this article

On the Semigroup Whose Elements Are Subgraphs of a Complete Graph

Author

Listed:
  • Yanisa Chaiya

    (Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University (Rangsit Campus), Pathum Thani 12121, Thailand)

  • Chollawat Pookpienlert

    (Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Nuttawoot Nupo

    (Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Sayan Panma

    (Center of Excellence in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

Abstract

Let K n be a complete graph on n vertices. Denote by S K n the set of all subgraphs of K n . For each G , H ∈ S K n , the ring sum of G and H is a graph whose vertex set is V ( G ) ∪ V ( H ) and whose edges are that of either G or H , but not of both. Then S K n is a semigroup under the ring sum. In this paper, we study Green’s relations on S K n and characterize ideals, minimal ideals, maximal ideals, and principal ideals of S K n . Moreover, maximal subsemigroups and a class of maximal congruences are investigated. Furthermore, we prescribe the natural order on S K n and consider minimal elements, maximal elements and covering elements of S K n under this order.

Suggested Citation

  • Yanisa Chaiya & Chollawat Pookpienlert & Nuttawoot Nupo & Sayan Panma, 2018. "On the Semigroup Whose Elements Are Subgraphs of a Complete Graph," Mathematics, MDPI, vol. 6(5), pages 1-10, May.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:5:p:76-:d:145441
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/6/5/76/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/6/5/76/
    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:6:y:2018:i:5:p:76-:d:145441. 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.