Conjectures About Wheels Without One Edge with Paths and Cycles

Michal Staš () and Mária Timková
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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

Mathematics, 2024, vol. 12, issue 22, 1-12

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.

Keywords: crossing number; join product; separating cycle; wheel; path; cycle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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