My mother has ascending aortic aneurysm size of aorta 3.7cm . she is traveling from india to usa next week. what are the risks? should she not travel?

Impossible to answer: Since an aneurysm can rupture or dissect at any time or not at all, there is no way to predict the complications. I don't think air travel per se increases the risk for the complications but certainly if they do come there will be no immediate treatment available. You and she will have to discuss the risk however small.

Go ahead: That's a pretty small aneurysm. I see no reason why she can't travel.