On the crossing numbers of Cartesian products of paths with special graphs

There are known exact results of the crossing numbers of the Cartesian product of all graphs of order at most four with paths, cycles and stars. Moreover, for the path P-n, of length n, the crossing numbers of Cartesian products G rectangle P-n, for all connected graphs G on five vertices and for forty graphs G on six vertices are known. In this paper, we extend these results by determining the crossing numbers of the Cartesian products G rectangle P-n for six other graphs G of order six.