I would wait and send out "announcements" so they'll arrive on or after graduation. "Announcements" are not the same as "invitations."
I volunteer at graduation and every year we have people show up with announcements in hand trying to get in. Currently, students get 10 tickets each at our school. If you don't have a ticket, you don't get in. (This seems like a huge amount to me - when I was in high school, you only got FOUR tickets!)