  In an R-parity violating supersymmetric scenario, the lightest neutralino
$\tilde \chi^0_1$ is no longer a stable particle. We calculate the branching
ratio for the decay mode $\tilde \chi^0_1 \longrightarrow \nu \gamma$ which
occurs at the one-loop level. Taking into account bilinear as well as trilinear
lepton number violating interactions as the sources of R-parity violation, we
make a detailed scan of the parameter space, both with and without gaugino mass
unification and including the constraints on the neutrino sector from the
recent Superkamiokande results. This study enables one to suggest interesting
experimental signals distinguishing between the two types of R-parity breaking,
and also to ascertain whether such radiative decays can give rise to collider
signals of the type $\gamma \gamma$ + $\not {\rm E}$ from pair-produced
neutralinos.
