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Conjectures About Wheels Without One Edge with Paths and Cycles

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 Timková

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

Abstract

The crossing number cr ( G ) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main aim of this paper is to give the crossing numbers of the join products G * + P n and G * + C n for the connected graph G * obtained by removing one edge (incident with the dominating vertex) from the wheel W 5 on six vertices, and where P n and C n are paths and cycles on n vertices, respectively. Finally, we also introduce four new conjectures concerning crossing numbers of the join products of P n and C n with W m ∖ e obtained by removing one edge (of both possible types) from the wheel W m on m + 1 vertices.

Suggested Citation

  • Michal Staš & Mária Timková, 2024. "Conjectures About Wheels Without One Edge with Paths and Cycles," Mathematics, MDPI, vol. 12(22), pages 1-12, November.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3484-:d:1516384
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    References listed on IDEAS

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    1. Michal Staš, 2021. "The Crossing Numbers of Join Products of Paths and Cycles with Four Graphs of Order Five," Mathematics, MDPI, vol. 9(11), pages 1-13, June.
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