you can regardless of how much you work after graduation always (within 2 years after graduation) decide to use your graduate rights according to the "graduate" rule. There will be no further requirements you will need to fullfill. It is the education in it self that gives you the graduate rights.
However as you probably know the amount that unemployed graduates get in Unemployment benefit ("dagpenge") is less than the amount that insured unemployed workers get.
So for graduates, that have got there graduate rights registered in the A-kasse, there is a special rule saying that graduates can have their benefits amount recalculated after 6 months...but only if the graduate have finished (lose/or quit) a work after the date of graduation, and only if the graduate has at least 3 months of income registered in the Income-register ("Indkomstregistret").
So you can always get the graduate amount, but if you work for 3 months (it is not an requirement that it need to be full time job), then you - as said - can get a higher amount in Unemployment benefits.
We recommend you to ask your A-kasse, if your part-time is enough, i.e. how many hours you must at least work during the 3 months period, for having the right to get af recalculation after 6 months. If you are interested in that off course.