  We consider the topological defects and spin structures of spin-1
Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) and
dipole-dipole interaction (DDI) in a rotating harmonic plus quartic trap. The
combined effects of SOC, DDI and rotation on the ground-state phases of the
system are analyzed. Our results show that for fixed rotation frequency
structural phase transitions can be achieved by adjusting the magnitudes of the
SOC and DDI. A ground-state phase diagram is given as a function of the SOC and
DDI strengths. It is shown that the system exhibits rich quantum phases
including vortex string phase with isolated density peaks (DPs), triangular
(square) vortex lattice phase with DPs, checkerboard phase, and stripe phase
with hidden vortices and antivortices. For given SOC and DDI strengths, the
system can display pentagonal vortex lattice with DPs, vortex necklace with
DPs, and exotic topological structure composed of multi-layer visible vortex
necklaces, a hidden giant vortex and hidden vortex necklaces, depending on the
rotation frequency. In addition, the system sustains fascinating novel spin
textures and skyrmion excitations, such as an antiskyrmion pair,
antiskyrmion-half-antiskyrmion (antiskyrmion-antimeron) cluster,
skyrmion-antiskyrmion lattice, skyrmion-antiskyrmion cluster,
skyrmion-antiskyrmion-meron-antimeron lattice, double-layer half-antiskyrmion
necklaces, and composite giant-antiskyrmion-antimeron necklaces.
