Final answer:
Thiopental should not be used in Greyhounds due to their unique physiology that can lead to prolonged recovery times from this barbiturate. Other drugs like propofol and morphine are generally considered safe for this breed.
Step-by-step explanation:
The drug that should not be used in Greyhounds among the ones listed is Thiopental. Greyhounds have a unique physiology compared to other dog breeds, which affects how they metabolize certain drugs. Thiopental is a barbiturate used for induction of anesthesia. Due to their low body fat and unique liver metabolism, Greyhounds can have prolonged recovery times from thiopental, making it a less suitable choice for this breed. Other drugs listed, such as propofol and morphine, are generally considered safe for use in greyhounds, and Ivermectin is not an anesthetic but an antiparasitic, although at high doses it can be dangerous for some breeds, but not specifically for Greyhounds.