Carry out the Kruskal MST algorithm on the weighted undirected graph below. 3.0 2.0 7.0 5. 08.07 (E) 10 8.0 1. (10 points) Show the disjoint sets of vertices just before each edge is considered. Do not forget to include sets with only one vertex. Use circles or ovals around the vertices in one set, and list the vertices with the leader first as done in lecture and sections. Indicate whether each edge is taken to be part of the eventual MST or is discarded. In case of ties on weight, use alphabetical vertex order. Continue with the updated disjoint sets in a new diagram, and the next chosen edge, and so on, until the MST is complete. 2. (5 points) Explain how the algorithm can be opportunistic by not considering some of the edges in some cases. Were there some edges it did not need to consider in this problem? What is the smallest number of edges it must consider? 3. (5 points) Illustrate (partly) how the MST that was found obeys the Minimum Spanning Tree Property using the two lightest edges not in the MST. Carry out the Kruskal MST algorithm on the weighted undirected graph below. 3.0 2.0 7.0 5. 08.07 (E) 10 8.0 1. (10 points) Show the disjoint sets of vertices just before each edge is considered. Do not forget to include sets with only one vertex. Use circles or ovals around the vertices in one set, and list the vertices with the leader first as done in lecture and sections. Indicate whether each edge is taken to be part of the eventual MST or is discarded. In case of ties on weight, use alphabetical vertex order. Continue with the updated disjoint sets in a new diagram, and the next chosen edge, and so on, until the MST is complete. 2. (5 points) Explain how the algorithm can be opportunistic by not considering some of the edges in some cases. Were there some edges it did not need to consider in this problem? What is the smallest number of edges it must consider? 3. (5 points) Illustrate (partly) how the MST that was found obeys the Minimum Spanning Tree Property using the two lightest edges not in the MST