Consider the following graph G = (V, E), where each edge e = (u, v) has a weight w(u, v), V = {a, b, c, d, e} and E = {(a, b), (b, c), (c, d), (d, a), (b, e), (c, e), (d, e)}. The weights on the edges are: We define the profile of a graph G to be the list of its edge weights in non-decreasing order. For example, in the graph G above, the profile is 1, 1, 2, 2, 3, 3, 3. The profile of an MST T is the list of its edge weights in non-decreasing order. Find every MST T for the graph G above: list the edges in alphabetical order, give the weight of T and its profile p. We know that the weights of all the MSTs, by definition, must be the same. Based on the results can you make a conjecture about profiles of MST's