please answer all three a.) When using Dijkstra’s Shortest Path Algorithm, which graph representation (adjacency matrix, adjacency list, edge list) would be most efficient to use?  b.) When using the Bellman-Ford Algorithm, which graph representation (adjacency matrix, adjacency list, edge list) would be most efficient to use? c.) When using the Floyd-Warshall Algorithm, which graph representation (adjacency matrix, adjacency list, edge list) would be most efficient to use?

Please use Breadth- First Search (BFS) algorithm and convert the graph for the vertices in the odd level in one color and the vertices in the even level in the other color

Apply Dijkstra's algorithm on the following graph. Show all the steps. F Start 10 B 15 12 15 D 2 10 E

1. a. b. Using the provided graph, answer the following questions c./ 90 140 60 D 120 B 90 50 50 100 80 110 100 E 80 40 60 90 F Provide the MST generated using Kruskal's algorithm showing the order with which edges were added in Provide the MST generated using Prim's algorithm showing how the order of which edges were added in step by step Provide the overall weight of the MST generated from the following graph using Kruskal's algorithm

Please help me with number 2 on this Discrete II Problem. Thank you.

1. Consider the weighted, directed graph containing the following vertices and edges.(Weights are in the parentheses.)Vertices: {A, B, C, D} Edges: {AB(5), BC(3), CA(4), AD(2), DA(4), CB(3)}a. Starting at vertex C, determine the shortest path tree using Dijkstrab. If you were to apply Floyd-Warshall’s algorithm to this tree, would it include the shortest path tree you found using Dijkstra? Why or why not?c. Starting at vertex C, determine the minimum spanning tree using Prim.d. Would Kruskal’s algorithm always result in the same MST as Prim’s? Why or why not?   Please provide graphs if possible.

Using Python, include written explanations of your conclusions. 1. Calculate the Laplacian of each of the graphs. 2. Calculate the eigenvalues of each of the graphs. 3. Use Kirchhoff's matrix tree theorem to count the number of spanning trees in each of the graphs. 4. Use the calculations you have completed to determine which of the graphs are connected. (v) Dodecahedron

Estimate the biggest graph with E = 10V that your computer and programming system could manage in 10 seconds if you used Dijkstra's technique to compute all of its shortest routes.

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.

There are many applications of Shortest Path Algorithm. Consider the problem of solving a jumbled Rubik's Cube in the fewest number of moves. I claim that this problem can be solved using a Shortest Path Algorithm. Determine whether this statement is TRUE or FALSE. NOTE: if you want to check if this statement is TRUE, think about how the Rubik's Cube Problem can be represented as a graph. What are the vertices? Which pairs of vertices are connected with edges? What is your source vertex and what is your destination vertex? How would Dijkstra's Algorithm enable you to find the optimal sequence of moves to solve a jumbled cube in the fewest number of moves?