I have a weighted undirected complete graph. I want to create a minimal Star forest of it which the total sum of weights of edges should be minimal. Star graph is a special type of graph in which m-1 vertices have degree 1 and a single vertex have degree m – 1. In other words, I am looking for minimal spanning forest of a complete graph that each tree in the forest is a star graph. The point is I have a constrain that the size of each star graph should not be less than K.
I am wondering if someone else solve this problem or know about a paper that explain it. Thanks in advance.