  We investigate the properties of quantized vortices in a dipolar
Bose-Einstein condensed gas by means of a generalised Gross-Pitaevskii
equation. The size of the vortex core hugely increases by increasing the weight
of the dipolar interaction and approaching the transition to the supersolid
phase. The critical angular velocity for the existence of an energetically
stable vortex decreases in the supersolid, due to the reduced value of the
density in the interdroplet region. The angular momentum per particle
associated with the vortex line is shown to be smaller than $\hbar$, reflecting
the reduction of the global superfluidity. The real-time vortex nucleation in a
rotating trap is shown to be triggered, as for a standard condensate, by the
softening of the quadrupole mode. For large angular velocities, when the
distance between vortices becomes comparable to the interdroplet distance, the
vortices are arranged into a honeycomb structure, which coexists with the
triangular geometry of the supersolid lattice and persists during the free
expansion of the atomic cloud.
