The crossing number of P(3,1)×PnP(3,1)×Pn

There are several known exact results on the crossing numbers of Cartesian products of paths, cycles, and complete graphs. In this paper we prove that the crossing number of Cartesian product between a path on n   vertices, PnPn and a special case of Petersen graph P(3,1)P(3,1), P(3,1)×PnP(3,1)×Pn is 4(n-1)4(n-1) for n⩾1n⩾1.