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 $C_n$.