What is the relationship between the current king of Thebes and the deceased king in Oedipus Rex by Sophocles?
This question is in a certain way the crux of the play. The easy and obvious answer is that Oedipus, the current ruler of Thebes, is the son of Laius, the previous king. This answer masks, though, an essential shading in the correct Greek terminology.
Lauis was the king or "basileus" of Thebes, i.e. a legitimate hereditary ruler. When Oedipus arrives in Thebes, he is made a ruler by popular acclaim. The correct term for absolute ruler by popular acclaim in Greek is "tyrranos" (English: tyrant). The actual Greek title of the play is "Oedipus Tyrranos". The great irony of the play is that Oedipus only discovers that he was the legitimate king, or basileus, at the end of the play, when Oedipus renounces his role as tyrant and exiles himself for the city's good, saying:
But never let my father’s city be condemned
to have me living here while I still live.
Let me make my home up in the mountains