Since he graduated in May, and was under the age of 24 on Dec 31 of the 2021 tax year, he could qualify as your dependent. Understand that if he qualifies as your dependent, then "you the parent" have the choice to claim him, or not claim him. However, the student "does not" have a choice and must select the option for "I can be claimed on someone else's tax return", weather you actually claim him or not.
Here's the rules, gisted from IRS Publication 17:
If the student:
Is under the age of 24 on Dec 31 of the tax year and:
Is enrolled in an undergraduate program at an accredited institution and:
Is enrolled as a full time student for any one academic semester that begins during the tax year, (each institution has their own definition of a full time student) and:
the STUDENT did NOT provide more that 50% of the STUDENT’S support (schollarships/grants received by the student ***do not count*** as the student providing their own support)
Then:
The parents qualify to claim the student as a dependent on the parent's tax return . Period, End of Story. But one thing I want to point out here. The parents *QUALIFY* to claim the student. The parents are *NOT* required to claim the student as a dependent. But even if they don’t, since they *qualify* to claim the student, then if the student will be filing their own tax return the student is *REQUIRED* to select the option for “I can be claimed on someone else’s return”. To reiterate:
If the student qualifies to be claimed on the parent’s tax return, then the student can not take the self-exemption on their own tax return, no …matter…what.
Now, since he graduated in May, it is perfectly feasible that your son "DID" provide more than 50% of his own support for the entire tax year. If so, then you do not qualify to claim him as a dependent on your tax return.
