[Solved] Homework 5 Solution

1. Execute Prim’s minimum spanning tree algorithm by hand on the graph below showinghow the data structures evolve specifically indicating when the distance from a fringevertex to the tree is updated. Clearly indicate which edges become part of the minimumspanning tree and in which order. Start at vertex A.

2. Execute Kruskal’s algorithm on the weighted tree shown below. Assume that edges ofequal weight will be in the priority queue in alphabetical order. Clearly show whathappens each time an edge is removed from the priority queue and how the dynamicequivalence relation changes on each step and show the final minimum spanning tree thatis generated.

3. Give an example of a weighted graph for which the minimum spanning tree is unique.Indicate what the minimum spanning tree is for that graph. Give another example of aweighted graph that has more than one minimum spanning tree. Show two differentminimum spanning trees for that graph. What determines whether a graph has more thanone minimum spanning tree?4. Given the following adjacency lists (with edge weights in parentheses) for a directedgraph:A: B(5), C(3), D(1)B: C(1), D(3)C: B(3), D(7), E(1)D: A(6), C(3)E: F(5)F: D(3), A(4)Execute Dijkstra’s shortest-path algorithm by hand on this graph, showing how the datastructures evolve, with A as the starting vertex. Clearly indicate which edges become partof the shortest path and in which order.