The pairing with Parashah Miketz, whose central episode is Joseph correctly interpreting Pharaoh's dreams of seven fat and seven lean cows and rising to administer Egypt's famine preparation as a direct result, rests on a shared theme rather than a shared vocabulary: both accounts concern wisdom granted specifically to govern well, demonstrated through a case others could not resolve on their own.
Joseph's wisdom is shown through correct dream interpretation, seeing meaning in symbols that Pharaoh's own magicians and wise men could not decipher, while Solomon's wisdom is shown through a different kind of insight entirely, seeing the truth behind two contradictory claims that no ordinary evidence could settle, yet both narratives present the gift as coming from God rather than from the recipient's own native cleverness, and both immediately install the wise figure in a position of governing authority as a direct consequence.
The parallel extends to how each account closes: Joseph's interpretation leads directly to Pharaoh elevating him over all of Egypt, and Solomon's judgment leads directly to all Israel hearing of it and holding him in awe as a king with wisdom to execute justice, both narratives using a single demonstrated case of insight as proof that a much larger administrative trust has been rightly placed in one person's hands.