It is generally recommended to wait at least six months after the hair transplantation surgery before dyeing your hair. This waiting period allows sufficient time for the transplanted hair to fully grow and stabilize. Dyeing the hair too soon after the surgery may potentially irritate the scalp or interfere with the healing process. It is always best to consult with your doctor or hair transplant specialist for personalized advice regarding when it is safe to dye your hair after the surgery.