Determining crossing number of join of the discrete graph with two symmetric graphs of order five
Summary: The main aim of the paper is to give the crossing number of the join product \(G + D_n\) for the disconnected graph \(G\) of order five consisting of one isolated vertex and of one vertex incident with some vertex of the three-cycle, and \(D_n\) consists of \(n\) isolated vertices. In the proofs, the idea of the new representation of the minimum numbers of crossings between two different subgraphs that do not cross the edges of the graph \(G\) by the graph of configurations \(\mathcal{G}_D\) in the considered drawing \(D\) of \(G + D_n\) will be used. Finally, by adding some edges to the graph \(G\), we are able to obtain the crossing numbers of the join product with the discrete graph \(D_n\) and with the path \(P_n\) on \(n\) vertices for three other graphs.
scientific article; zbMATH DE number 7078091