So guys i want to find a mathematic formulation to use in GLPK. Given a directed graph and a root, i need to find a tree that minimizes the value of the edges in that graph. Note that we DON'T need to include all vertices.

In that example the root is A and the tree that minimizes the cost os edges are A,C,E,D with -4 cost. In other words i want to find a tree with minimum value, the number of nodes doesn't matter at all.

Instance: Given a directed graph  G = (V, A) with weights "wa" ∈ R in edges and a root v ∈ V.

Solution: A directed tree with root in v.

Objective: Minimize total weight.

Any help with correlate problems? I can't find any material or papers...