Given is a graph G of n+1 vertices, which is constructed as follows: initially there is only one vertex v, and one a move we can add a vertex and connect it to exactly one among the previous vertices. The vertices have non-negative real weights such that v has weight 0 and each other vertex has a weight not exceeding the avarage weight of its neighbors, increased by 1. Prove that no weight can exceed n2. combinatoricsgraph theoryalgebraKvant