On the Crossing Numbers of the Joint Graphs of a Path or a Cycle

Abstract

The crossing number problem is in the forefront of topological graph theory. At present, there are only a few results concerning crossing numbers of join of some graphs. In this paper, for the special graph \(Q\) on six vertices, we give the crossing numbers of its join with \(n\) isolated vertices, as well as with the path \(P_n\) on \(n\) vertices and with the cycle \(C_n\).