IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i10p1694-d1661291.html
   My bibliography  Save this article

Exploring the Crossing Numbers of Three Join Products of 6-Vertex Graphs with Discrete Graphs

Author

Listed:
  • Michal Staš

    (Department of Mathematics and Theoretical Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, 042 00 Košice, Slovakia)

  • Mária Švecová

    (Department of Mathematics and Theoretical Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, 042 00 Košice, Slovakia)

Abstract

The significance of searching for edge crossings in graph theory lies inter alia in enhancing the clarity and readability of graph representations, which is essential for various applications such as network visualization, circuit design, and data representation. This paper focuses on exploring the crossing number of the join product G * + D n , where G * is a graph isomorphic to the path on four vertices P 4 with an additional two vertices adjacent to two inner vertices of P 4 , and D n is a discrete graph composed of n isolated vertices. The proof is based on exact crossing-number values for join products involving particular subgraphs H k of G * with discrete graphs D n combined with the symmetrical properties of graphs. This approach could also be adapted to determine the unknown crossing numbers of two other 6-vertices graphs obtained by adding one or two additional edges to the graph G * .

Suggested Citation

  • Michal Staš & Mária Švecová, 2025. "Exploring the Crossing Numbers of Three Join Products of 6-Vertex Graphs with Discrete Graphs," Mathematics, MDPI, vol. 13(10), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1694-:d:1661291
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/10/1694/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/10/1694/
    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:13:y:2025:i:10:p:1694-:d:1661291. 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.