We consider a binary dipolar Bose-Einstein condensate with repulsive contact and dipolar interactions under rotation. Our results show that the interplay among short-range interaction, long-range interaction, and rotation can give rise to a rich variety of topological configurations, including giant skyrmions with multiply topological charges and skyrmion-vortex lattices. In particular, we find
... [Show full abstract] that for fixed rotation frequencies, tuning the short- and long-range interactions can derive novel ground-state phases, such as a meron pair composed of two fractional skyrmions and a skyrmion with topological charge Q=2 centered in giant skyrmions.