The toroidal crossing number of K4,nK4,n

In this paper, we show that the toroidal crossing number of K4,nK4,n, K1,3,nK1,3,n, K2,2,nK2,2,n, K1,1,2,nK1,1,2,n and K1,1,1,1,nK1,1,1,1,n is ⌊n4⌋[2n−4(1+⌊n4⌋)]. In addition, a new lower bound for the toroidal crossing number of Km,nKm,n has been obtained. We also discuss about the crossing number of K4,nK4,n in the general surfaces.