There is nothing illegal about an adult former student inviting a former teacher on a date. But some schools and school districts would disapprove of the judgment shown by a former teacher who agreed to the invitation, and that
Can teachers sleep with students after they graduate?
Yes, but it is a growing taboo, at least in America. It is to the point that some states have passed or considered laws forbidding teachers to have any sexual relations with students until they have graduated for at least a year, regardless of age.
Is it OK for a college professor to date a student?
At many schools, there are no formal rules about professors dating students. It is discouraged, but not prohibited. For most educators, there is an unwritten rule that getting involved with students is a bad idea. It is usually suggested that no professor should date a student in his class.