How can I deduct expenses for graduate applications? Can I put them under books and materials required?

Sorry---applications to schools are not a qualified education expense.

QUALIFIED EDUCATION EXPENSES

https://ttlc.intuit.com/questions/1899852-what-are-considered-qualified-education-expenses

https://ttlc.intuit.com/questions/2976047-what-are-examples-of-education-expenses

You can't deduct graduate school or undergraduate application fees. You will find a good list of  what is and is not a qualified education expense in IRS Pub. 970, Tax Benefits For Education at this link:
 

IRS Pub 970 Tax Benefits for Education

This question was previously answered in 2019 here:  https://ttlc.intuit.com/community/college-education/discussion/can-i-deduct-school-application-expenses/00/506604 

I suggest you read it.

However, Publication 970 Tax Benefits for Education 2021, Page 13 states

"Qualified Education Expenses:   For purposes of the American Opportunity Credit, qualified education expenses are tuition and certain related expenses required for enrollment or attendance at an eligible
educational institution."

My personal interpretation of this is that the application fee for the college you attend would be a Qualified Education Expense because schools require an application fee to enroll and attend their institution. 

Application fees for those schools you decide not to attend would not qualify. 

Likewise, travel expenses would not be a Qualified expense.

Publication 970B is available here:  https://www.irs.gov/forms-pubs/about-publication-970 click on the link to the Current Revison  PDF.

NOTE:  This assumes you meet the qualifications to claim the American Opportunity Credit, which are detailed on Page 11 of the same Publication.  If you do not qualify for this credit, you may qualify for the Lifetime Learning Credit, which is explained starting on page 21 of the Publication.  The Lifetime Learning Credit requires receipt of Form 1098-T.  It seems to me that your application fee is not deductible for the Lifetime Learning Credit.

**Disclaimer:  The above is my personal interpretation of the Publication and may or may not be correct.