The crossing number of

Abstract: The exact crossing number is known only for a few specific families of graphs. Cartesian products of two graphs belong to the first families of graphs for which the crossing number has been studied. Let be a path with vertices. , the -power of the graph , is a graph on the same vertex set as and the edges that join two vertices of if the distance between them is at most . Very recently, some results concerning crossing numbers of were obtained. In this paper, the crossing numbers of the Cartesian product of with the cycle are studied. It is proved that the crossing number of the graph is , and the upper bound for the crossing number of the graph is given. [Copyright &y& Elsevier]