What is the ruling on a woman sitting next to a man on a plane when she is traveling without a mahram?

A woman's travel without a mahram is not permissible except in cases of necessity. It is also forbidden for her to sit in close proximity to a non-mahram man. If there was no valid excuse for her travel, or if she had the option to sit next to a woman but did not, then she has done wrong and must repent.