Answer:
Ptolemy Philadelphus, with whom Ashoka had diplomatic relations, was the ruler of Egypt. Ptolemy Philadelphus was a Greek king who ruled over the Ptolemaic Kingdom of Egypt from 283 to 246 BCE. He was the son of Ptolemy I Soter, the founder of the Ptolemaic dynasty, and Berenice I.

Background: Ptolemaic Kingdom
The Ptolemaic Kingdom was a Hellenistic kingdom based in Egypt. It was founded in 305 BCE after the death of Alexander the Great, when his general Ptolemy I Soter declared himself Pharaoh and established the Ptolemaic dynasty. The Ptolemies ruled Egypt for nearly three centuries until the kingdom fell to the Roman Empire in 30 BCE.

Ptolemy Philadelphus and Ashoka
Ashoka was an emperor of the Maurya Empire in ancient India, who ruled from 268 to 232 BCE. He was known for his military conquests and later converted to Buddhism, becoming a proponent of non-violence and spreading the teachings of Buddha.

During his reign, Ashoka sought to establish diplomatic relations with various rulers and empires. One of the rulers he had diplomatic relations with was Ptolemy Philadelphus of Egypt. This is mentioned in Ashoka's Rock Edict XIII, where he expresses his desire for friendly relations with the Greek kings, specifically mentioning Ptolemy Philadelphus.

Importance of Diplomatic Relations
Establishing diplomatic relations with other kingdoms and empires was an important aspect of ancient diplomacy. It allowed for the exchange of goods, ideas, and cultural influences between different regions. Diplomatic relations also promoted peace and stability, reducing the likelihood of conflicts and wars.

In the case of Ashoka and Ptolemy Philadelphus, their diplomatic relations may have facilitated trade and cultural exchanges between the Maurya Empire and the Ptolemaic Kingdom. It is likely that there were exchanges of goods such as spices, textiles, and precious metals, as well as cultural exchanges in the form of art, literature, and ideas.

Overall, the diplomatic relations between Ashoka and Ptolemy Philadelphus were significant in promoting peaceful interactions, trade, and cultural exchanges between the Maurya Empire and the Ptolemaic Kingdom of Egypt.