The crossing numbers of Cartesian products of paths with 5-vertex graphs Original Research Article

For two graphs defined from K5 by removing one edge or two nonadjacent edges we prove that the crossing number of Cartesian product of the graph with the path of length n is 4n and 3n−1, respectively. These results complete the crossing numbers list of Cartesian products of all 5-vertex graphs with paths. We also give a description of Cartesian products of 5-vertex graphs with cycles and stars, whose crossing numbers are known.