My child got a job after graduation in June this year. So now for this year 2015 taxes will she be considered partially dependent? Also, the W-4 changes will be applicable after June only?

Thanks.

There is no such thing as "partially dependent." If she is at least 19 as of December 31 and either provided more than half of her own financial support for the year or has earned more than $3800, she is not your dependent.

As for any changes you make to your W-4: changes in withholding are not automatic - you must submit an updated W-4 form to your payroll department, and the new withholding should start with the next pay check after that.

Actually, irrespective of her income, you CAN claim your child as a dependent if you supported said child while she was in school AND the schooling lasted at least five months.

You need to discuss this with her to ensure you BOTH do not claim her exemption.