Is international graduate student with a F1 visa out of status after graduation?

Yes, an international graduate student with an F-1 visa is automatically out of status after their program completion date as listed on their I-20 form, unless they have a valid extension or have begun another F-1 program. The F-1 visa is tied to the specific program of study. Once that program ends, the visa's validity for that purpose ends as well. They then have a grace period (generally 60 days) to depart the United States or take specific actions (like applying for Optional Practical Training (OPT) or a change of status) to remain legally. Failing to do so within the grace period results in being out of status.