  We study the properties of singly-quantized linear vortices in the supersolid
phase of a dipolar Bose-Einstein condensate at zero temperature modeling
$^{164}$Dy atoms. The system is extended in the $x-y$ plane and confined by a
harmonic trap in the the polarization direction $z$. Our study is based on a
generalized Gross-Pitaevskii equation. We characterize the ground state of the
system in terms of spatial order and superfluid fraction and compare the
properties of a single vortex and of a vortex dipole in the superfluid phase
(SFP) and in the supersolid phase (SSP). At variance with a vortex in the SFP,
which is free to move in the superfluid, a vortex in the SSP is localized at
the interstitial sites and does not move freely. We have computed the energy
barrier for motion from an equilibrium site to another. The fact that the
vortex is submitted to a periodic potential has a dramatic effect on the
dynamics of a vortex dipole made of two counter rotating parallel vortices;
instead of rigidly translating as in the SFP, the vortex and anti-vortex
approach each other by a series of jumps from one site to another until they
annihilate in a very short time and their energy is transferred to bulk
excitations.
