Final answer:
The trochlear (IV) and abducens (VI) cranial nerves each innervate one eye muscle responsible for specific movements of the eye. The oculomotor (III) nerve, however, controls multiple eye muscles and the trigeminal (V) nerve is not involved in eye muscle innervation.
Step-by-step explanation:
The cranial nerves that innervate only one eye muscle are the trochlear (IV) nerve, which controls the superior oblique muscle, and the abducens (VI) nerve, which controls the lateral rectus muscle. The oculomotor (III) nerve is not an answer choice since it innervates multiple eye muscles, not just one. The trigeminal (V) nerve is primarily responsible for facial sensation and mastication muscles, hence not involved in innervating any eye muscles. Therefore, the correct answer is the abducens (VI) nerve which innervates only the lateral rectus muscle.