Can we examine Robert Frost's "The Road Not Taken" in light of Freud's "Oedipus Complex" theory?
This is an interesting question, but I think the story of Oedipus as told in Sophocles' Oedipus the King would be a more apt comparison than Freud's Oedipus Complex.
Freud's theory was inspired by Jocasta's statement in Oedipus the King that all men have had dreams in which they have slept with their mothers. Freud, in his Interpretation of Dreams, expressed the belief that all males desired their mothers sexually and, because they viewed their fathers as sexual rivals, wanted to kill their fathers. Sexual desire, though, and a desire to kill one's father strikes me as having no place in Frost's poem.
Frost's poem does, however, recall the situation that Oedipus found himself in when he did kill his father (Laius), because this event occurred "at a place where three roads meet" (line 861 in Johnston's translation).
Frost's situation is different from Oedipus', though, because Frost is unsure about which road to take. Frost could have taken either road, but he chose to take "the one less traveled by." Sophocles gives us no indication that Oedipus deliberated about which road to take. Oedipus was simply trying to avoid his parents, whom he mistakenly thought lived in Corinth. It just so happened that Oedipus' father was travelling the same road and a hostile altercation between the two men led to Oedipus unwittingly killing his father.
So, whereas Frost seems to have had a choice about which road he could have taken, Oedipus was not faced with a similar choice. Had Oedipus happened to have chosen a different road that still probably would not have made any difference because his destiny eventually would have caught up with him on another road.