The Crossing Number of Cartesian Products of Stars with 5-Vertex Graphs

Garey and Johxon have proved that the problem to determine the crossing number of graphs is NP-complete. Because of its difficulty, presently we only know the crossing number of some classes of special graphs. The crossing number of cartesian products of paths and cycles with 5-vertex graphs mostly are known, but only few cartesian products of 5-vertex graphs with star K_1,n are known. In this paper, we extent those results,and determine the crossing numbers of cartesian products of two 5-vertex graphs with star K_1,n.