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

Michal Staš () and Mária Švecová
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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 Švecová: Department of Mathematics and Theoretical Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, 042 00 Košice, Slovakia

Mathematics, 2025, vol. 13, issue 10, 1-15

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 * .

Keywords: crossing number; discrete graphs; good drawing; join product; paths; redrawing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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