Which of the following nerves is part of the innervation of the liver?

The right vagus nerve plays a significant role in the innervation of the liver. It carries parasympathetic fibers from the brainstem, which are essential for regulating the functions of the liver, including the stimulation of bile production and secretion. These fibers contribute to the autonomic nervous system's control over the digestive processes, helping to promote liver function during the digestive phase.

In contrast, the other options do not directly innervate the liver in the same way. Although the left phrenic nerve is associated with diaphragm innervation and contributes to sensation from the diaphragm, it does not innervate the liver. The lesser splanchnic nerve is primarily involved in innervating the adrenal glands and kidneys, rather than the liver specifically. The pelvic splanchnic nerve primarily provides innervation to the lower pelvic organs and is not functionally related to liver innervation.