  In this letter we investigate the effects of dipole-dipole interactions on
the vortex lattices in fast rotating Bose-Einstein condensates. For single
planar condensate, we show that the triangular lattice structure will be
unfavorable when the s-wave interaction is attractive and exceeds a critical
value. It will first change to a square lattice, and then become more and more
flat with the increase of s-wave attraction, until the collapse of the
condensate. For an array of coupled planar condensates, we discuss how the
dipole-dipole interactions between neighboring condensates compete with the
quantum tunneling processes, which affects the relative displacement of two
neighboring vortex lattices and leads to the loss of phase coherence between
different condensates.
