  The strong coupling constants of spin-3/2 to spin-1/2 doubly heavy baryon
transitions with light vector mesons are estimated within the light-cone QCD
sum rules method. Moreover, using the vector-meson dominance ans\"atz, the
widths of radiative decays $B_{QQ}^* \to B_{QQ} \gamma$ are calculated. The
results for the said decay widths are compared to the predictions of other
approaches.
