Lost Graph

Mike is given an undirected graph G of N vertices and M edges. A non-negative integer Xi is assigned to the i'th vertex of G, for 1 ≤ i ≤ N. Mike was asked to assign labels to each edge of the graph so that the following condition is satisfied: Let's suppose that the j'th edge of G connects vertices Uj and Vj. Then, a non-negative integer Yj equals to XUj xor XVj. This challenge was too easy fo