  Stable vortex dimers are known to exist in coherently coupled two component
Bose-Einstein condensates (BECs). We construct stable vortex trimers in three
component BECs and find that the shape can be controlled by changing the
internal coherent (Rabi) couplings. Stable vortex N-omers are also constructed
in coherently coupled N-component BECs. We classify all possible N-omers in
terms of the mathematical graph theory. Next, we study effects of the Rabi
coupling in vortex lattices in two-component BECs. We find how the vortex
lattices without the Rabi coupling known before are connected to the Abrikosov
lattice of integer vortices with increasing the Rabi coupling. In this process,
vortex dimers change their partners in various ways at large couplings. We then
find that the Abrikosov lattices are robust in three-component BECs.
