For Items 49-52. Refer to Graph 2 49.Using Prim's Algorithm to find the minimum spanning tree in Graph 2 and starting with vertex 2. The order of the first three (3) edges to be added on the graph could be: A. (2,6), (3,6), (6,9) C. (3,6), (6,9), (2,8) D. (3,6), (2,8), (6,9) B. (2,6), (6,9), (7,9) 50. What is the highest cost of the edge to be added in Graph 2 when finding the minimum spanning tree? A. 12 C. 11 B. 10 D. 16

Given the following graph, A C 3 1 E 4 В F 7 D 5 What is the next edge and vertex(s) to be included in the solution if a. we are using Prim's algorithm to find a minimum spanning tree and we have started with vertex E? Edge: Vertex(s): What is the next edge and vertex(s) to be included in the solution if b. we are using Kruskal's algorithm to find a minimum spanning tree Edge: Vertex(s): What is the next edge and vertex(s) to be included in the solution if c. we are using Dijkstra's shortest path algorithm to find shortest paths and we have started with vertex E, with C and F already included in the shortest path tree? Edge: Vertex(s):

Mark Zuckerberg, the CEO of Facebook, has hired you to lead the Facebook Algorithms Group. He has asked you to use various graph algorithms to analyze the world's largest social network. The Facebook Graph has 2.8 billion vertices, with each vertex being a Facebook user. Two vertices are connected provided those two users are "friends". The first decision you need to make is how you want to model the Facebook graph. Determine whether you should use an adjacency-list representation or an adjacency-matrix representation.

With a given graph below, run the Bellman-Ford Algorithm to find the shortest path from node s to all nodes.  For example,   (0, 100, 23, 300, 50)  for (node 1, node 2, node 3, node 4, node 5)

1. Use the graph below to answer the following questions. A B H 10 G 10 25 20 5 50 5 5 30 5 15 C 20 D F 15 E (a) Use Kruskal's Algorithm to produce a minimum spanning tree. Write down the edges that you choose in order of the algorithm. (b) Use Prim's Algorithm to produce a minimum spanning tree (assume A is the root/source). Write down the edges that you choose in order of the algorithm.

Using the Kruskal’s Algorithm, show the minimum spanning tree representation of the graph.