What is the ruling on offering condolences by raising the right hand instead of shaking hands after burial at the graveside? And should condolences be abandoned if this practice is an innovation?

It is sunnah (definition) to offer condolences to the afflicted in a way that comforts and brings patience to them. It is not restricted to a specific time or a particular form. It is permissible to accept condolences at the graveyard before or after burial. It is permissible for the family of the deceased to stand in a row to receive condolences, as this facilitates the reception of those offering condolences. As for gesturing with the hand for greeting instead of shaking hands, it is disliked (makruh (definition)) or forbidden (haram (definition)) because it goes against the established sunnah of shaking hands, unless abandoning it would lead to a greater harm.