Review of recent results about the k-centrum of a Tree

This paper is concerned with thekappa-centrum of a graph. This concept, related to a particular location problem, generalizes that of the center and that of the median of a graph: thekappa-centrum is the set of points for which the sum of the (weighted) distances from thekappa farthest vertices is minimized. The paper will review some recent results about this problem. In particular, some properties of cardinality, connectivity and, more generally, of the structure of thekappa-centrum of a weighted tree will be presented.