for being eligible for dagpenge after the graduate rule, you must have lived in Denmark right before you startet your education and again at latest 14 days after finishing education. If you lived in Malmö when you began at Lund University, then you can not get dagpenge as graduate in Denmark. I assume that you did not complete any kind of bachelor in Denmark before. ..the study at Lund University is a full education.
I am not sure about the rules for graduates in Sweden, but you should find out if you can get benefits as graduate from Sweden.
However if you continue to work in Denmark after graduation, while still living in Malmö, then you must sign Up with a danish A-kasse.
It is always in the country where you work, that you must be insured against unemployment.
However, in Denmark you can only get dagpenge after 1 year membership and if you have had a certain income that year (i.e. you can not get dagpenge after the graduate rule).
Anders Weber, www.a-kasser.dk