My parents want to claim educational expenses from my last year of college, however, they no longer claim me as a dependent. Cant they do that?

No.  If you do not qualify as their dependent, they are not allowed to claim a tuition credit, on your education.

But, be sure they can't claim you as a dependent.

Can the student be claimed as a dependent in the Graduation year? (answer written as if the parent asked the question)

If he/she was a student (under 24) for at least 5 months and lived with you for more than half the year, and did not provide more than 1/2 his own support for the whole year, you can still claim him. Be sure he knows you're claiming him, so he doesn't claim himself. He can only be claimed once. But, he can "file taxes" without claiming his own exemption.

The real question is who should be claiming him in this "transition" year to adulthood. You two have to agree on who is going to claim his exemption. Each should do their taxes both ways and see which way the family comes out best.  Even then, you have to meet the rules. 

There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit.

The rule is that a child of a taxpayer can still be a “Qualifying Child” dependent, regardless of his income, if:

1. he is a full-time student under 24 for at least 5 calendar months of the year (graduating in May usually means you meet the 5 month rule)
2. he did not provide more than 1/2 his own support  (scholarships are considered 3rd party support and not support provided by the student). 
3. lived with the parent (including time away at school) for more than half the year

So, it usually hinges on "Did he provide more than 1/2 his own support in 2022.

The support value of the home you provided is the fair market rental value of the home plus utilities & other expenses divided by the number of occupants. IRS Publication 501 on page 20 has a worksheet that can be used to help with the support calculation. See: http://www.irs.gov/pub/irs-pdf/p501.pdf  (page 15)

No.  Whoever claims the dependent claims the Educational expenses. You can file on your own and not claim yourself as a dependent, if all you want is to get a refund for what was withheld.

If a student is claimed as a dependent on another person's tax return, all qualified education expenses of the student are treated as having been paid by that person. Therefore, only that person can claim an education credit for the student. If a student is not claimed as a dependent on another person's tax return, only the student can claim a credit.