10. Suppose we have an undirected, connected, weighted graph with n vertices such that: . Every weight is an integer greater than zero. No two edges have the same weight (a) In terms of n, what is the lowest cost a minimum spanning tree (MST) could have for a graph with n nodes that meets the description above? (The cost of an MST for some n-node graphs meeting the description will be higher. The question here is what the lowest possible MST cost could be-you get to pick a graph that minimizes MST cost subject to the criteria.) Give a closed-form solution, which just means that, for full credit, your answer should not be in terms of a series. (b) Prove your answer to part (a) is correct for all n 2 1