IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i13p2960-d1185654.html
   My bibliography  Save this article

Crossing Numbers of Join Product with Discrete Graphs: A Study on 6-Vertex Graphs

Author

Listed:
  • Jana Fortes

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

  • Michal Staš

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

Abstract

Reducing the number of crossings on graph edges can be useful in various applications, including network visualization, circuit design, graph theory, cartography or social choice theory. This paper aims to determine the crossing number of the join product G * + D n , where G * is a connected graph isomorphic to K 2 , 2 , 2 ∖ { e 1 , e 2 } obtained by removing two edges e 1 , e 2 with a common vertex and a second vertex from the different partitions of the complete tripartite graph K 2 , 2 , 2 , and D n is a discrete graph composed of n isolated vertices. The proofs utilize known exact crossing number values for join products of specific subgraphs H k of G * with discrete graphs in combination with the separating cycles. Similar approaches can potentially estimate unknown crossing numbers of other six-vertex graphs with a larger number of edges in join products with discrete graphs, paths or cycles.

Suggested Citation

  • Jana Fortes & Michal Staš, 2023. "Crossing Numbers of Join Product with Discrete Graphs: A Study on 6-Vertex Graphs," Mathematics, MDPI, vol. 11(13), pages 1-10, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2960-:d:1185654
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/13/2960/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/13/2960/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gregory Fridman & Yuri Vasiliev & Vlada Puhkalo & Vladimir Ryzhov, 2022. "A Mixed-Integer Program for Drawing Orthogonal Hyperedges in a Hierarchical Hypergraph," Mathematics, MDPI, vol. 10(5), pages 1-15, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      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:11:y:2023:i:13:p:2960-:d:1185654. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.