I want to give Improvement Exam for class 12 next year. Can I also apply Graduation this year?

NO you cannot do graduation if you want to give improvement exam as it is not allowed by CBSE.
EVEN when you’ll fill the form for improvement exam, it has a declaration that the student must not have joined any higher degree programme , which is to be attested/signed/stamped by your school principle .
So , its clear that CBSE doesn’t allow this, but if you want to take some risks , its up to you.
Good Luck 🙂