8. Use Prim's algorithm and Kruskal's algorithm to find a minimum spanning tree for the weighted graph given below. 5 3. 3 7 e d f 6 3 8 4. h 4. 2. 4) 2.

[Problem 9] Starting at vertex A, run Prim's algorithm on the following graph. You do not need to draw all steps but you must display the final picture of the generated minimum spanning tree and the order of inclusion of edges into the tree, using standard notation (u,v) to represent an edge between hypothetical vertices u and v, in order to receive points. B A 1 2 D 3 F

b) Based on the depth-first search to create the minimum spanning tree for the following graph. (Assume that the vertices are selected in alphabetical order and the starting vertex is A) 6/7

2. Use the flow graph of K, to answer the following questions. 66 34 8/8 3:3 111 K₂ 2/2 a. Identify each edge and the capacity in graph K. Enter your answer in the space below the question. For example: d(s, 0) = 4 b. What is the Low into vertes a and the flow out ola? Flow into a.. Flow out of d- c. What is the flow into vertex & and the flow out of e? Flow into c- Flow out of c= d. What is the flow out of sources and the flow into ?? Flow into s- Flow out of t