Hey, the following question has been closed by OP, minutes after an answer had been posted. It is an interesting, quite simple yet not fully trivial question, with no similar post in MSE as far as I can tell. Would it be possible to undelete it ?
https://math.stackexchange.com/questions/3662615/graph-theory-graphs-whose-scores-are-arithmetic-sequences/3662653#3662653
https://math.stackexchange.com/questions/3662615/graph-theory-graphs-whose-scores-are-arithmetic-sequences/3662653#3662653