Disconnected spanning subgraphs of paths in the join products with cycles

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 of the cycles C_n 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.