Among many topological indices of trees the sum of distances sigma (T) and the number of subtrees F(T) have been a long standing pair of graph invariants that are well known for their negative correlation. That is, among various given classes of trees, the extremal structures maximizing one usually minimize the other, and vice versa. By introducing the "local" versions of these invariants, sigma(T) (nu) for the sum of distance from nu to all other vertices and sigma(T) (nu) for the number of subtrees containing nu, extremal problems can be raised and studied for vertices within a tree. This le...
