Please answer questions from v to vii.

Problem 1 (30 pts (4,4,4,4,4,4,6)]: Graph Algorithms Refer to the weighted graph below for the following problems. 21 10 16 23 17 20 19 i. List the vertices in the order they are visited in a Depth First Search that starts at vertex B. (Assume that DFS processes vertices alphabetically, when given the option of multiple vertices to explore.) ii. Give the path that is found frorn vertex B to vertex F using a Depth First Search. (Again assume that DFS processes vertices alphabetically, when given the option of multiple vertices to explore.) iii. List the vertices in the order they are visited in a Breadth First Search that starts at vertex B. (Assume that BFS processes vertices alphabetically, when given the option of multiple vertices to explore.) iv. Give the path that is found from vertex B to vertex F using a Breadth First Search. (Again assume that BFS processes vertices alphabetically, when given the option of multiple vertices to explore.) v. Suppose the given graph represents the layout of a town with nodes representing houses and edges paths between them. The weight of an edge represents the cost of paving the path. After a particularly rainy year the mayor of the city decides that people's shoes were getting too muddy and she decrees that the paths in the town must be paved such that it is possible to go from any one house to another without getting off of a paved path. Your assignment, as a Northeastern coop, is to recommend the lowes What is the total cost of your recommendation? What is the name of the network formed by the paved paths? t cost way to achieve the mayor's decree. vi. For the given graph list the edges in the order in which Prim's algorithm would add them starting with vertex B (your answer should be of the form 1.(A, B2.(B, D)...}.) vii. For the given graph list the edges in the order in which Kruskal's algorithm would add therm (your answer should be of the form f1.(A, B) 2.(B, )