Disconnected spanning subgraphs of paths in the join products with cycles

This is the authors' abstract. We don't add key points for this paper.

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 of the cycles Cn on n vertices with all nonempty disconnected spanning subgraphs of the paths P5 and P6 on five and six vertices, respectively. Recently, this problem was solved for the nonempty disconnected spanning subgraphs of the paths on three and four vertices by Klešč.