The crossing numbers of join products of K4 ∪ K1 with cycles

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Stas Michal; Timkova Maria

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Journal Paper

Paper Information

Journal: COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION Year:2025 | Volume:10 | Issue:4 Page(s): 933-948

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Title

The crossing numbers of join products of K4 ∪ K1 with cycles

Author(s)

Stas Michal | Timkova Maria | Issue Writer Certificate

Keywords

graph

crossing number

join product

separating cycle

cycle

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. In the paper, we extend known results concerning crossing numbers of join products of two small graphs with cycles. The crossing number of the join product G∗ + Cn for the disconnected graph G∗ consisting of the complete graph K4 and one isolated vertex is given, where Cn is the cycle on n vertices. The proof of the main result is done with the help of lemma whose proof is based on a special redrawing technique. Up to now, the crossing numbers of G + Cn are done only for a few disconnected graphs G. Finally, by adding new edge to the graph G∗, we are able to obtain the crossing number of G1 + Cn for one other graph G1 of order five.

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