  A search for the rare decays $W^{+}\rightarrow{D^{+}_{s}\gamma}$ and
$Z\rightarrow{D^{0}\gamma}$ is performed using proton-proton collision data
collected by the LHCb experiment at a centre-of-mass energy of 13 TeV,
corresponding to an integrated luminosity of 2.0 fb$^{-1}$. No significant
signal is observed for either decay mode and upper limits on their branching
fractions are set using $W^{+}\rightarrow{\mu^{+}\nu}$ and
$Z\rightarrow{\mu^{+}\mu^{-}}$ decays as normalization channels. The upper
limits are $6.5\times10^{-4}$ and $2.1\times10^{-3}$ at 95% confidence level
for the $W^{+}\rightarrow{D^{+}_{s}\gamma}$ and $Z\rightarrow{D^{0}\gamma}$
decay modes, respectively. This is the first reported search for the
$Z\rightarrow{D^{0}\gamma}$ decay, while the upper limit on the
$W^{+}\rightarrow{D^{+}_{s}\gamma}$ branching fraction improves upon the
previous best limit.
