What is the line of succession that resulted in Creon's ascension to power as referred to in Sophocles' Antigone?
The line of succession is alluded to in Antigone by Creon, but since Antigone is actually the final play of a trilogy, we must remember that the line of succession is actually better explained in the earlier plays. Creon particularly alludes to the line of succession in his first lines:
... And so, since in the same daythey [Oedipus's sons] both fell by twofold fate, each striking and spreading fratricidal pollution, now I hold
sole power and the throne. (170-173)
However, who Creon is is and how he came to power is better explained in the earlier plays.
Creon is the brother of Jocasta who was married to King Laius but after his death married Oedipus and made him king. As we learn in the first play of the trilogy, Oedipus Rex (Oedipus the King), Oedipus is actually the biological son of both Jocasta and Laius, which fulfilled a prophecy that Oedipus would one day commit incest with his mother. Also, King Laius was killed at a crossroads while traveling to Delphi, and it was Oedipus who killed him and his traveling companions who had attacked Oedipus, which also fulfills the prophecy that Oedipus would kill his own father. After Oedipus learns these things in Oedipus Rex, Jocasta kills herself, Oedipus steps down from the throne and Creon takes over.
In the second play of the trilogy, Oedipus at Colonus, we learn that at first Oedipus's two sons Polynices and Eteocles agree to let Creon rule in order to purge the city of the curse brought on by Oedipus's incest with Jocasta, as we see in Ismene's lines:
At the first they willed
To leave the throne to Creon, minded well
Thus to remove the inveterate curse of old. (Oedipus at Colonus)
However, apparently both sons became ambitious. The eldest son, Polynices takes the throne, but then the younger son Eteocles decides to fight him for it. He banishes his elder brother; then, Polynices returns with an army from Argos to try and recapture the throne, but both brothers die in the fight.
Since now both of Oedipus's male heirs are dead, leaving only his two daughters born of Jocasta, Antigone and Ismene, the next male in line to the throne is Creon, uncle to all four of Oedipus's children.
Therefore, the line of succession for the crown of Athens went from Oedipus, to Creon, to Polynices, to Eteocles due to usurpation, and then finally back to Creon.