5. For the Graph given below, illustrate the Floyd-Warshall algorithm to determine the final D and P matrices and determine the shortest path for the following source and destination. All answers must come from the final D and P matrices. a) From vertex 4 to 3 b) From vertex 3 to 1 2 2 6 3 5 7 12 3
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- Discrete math: (a) Apply improved Dijkstra’s algorithm to the following graph to find the shortest path from A to every other vertex in the graph. (b) Apply Kruskal’s algorithm to the graph to find a minimum spanning tree.4. Using Floyd's algorithm, compute the distance matrix for the weight directed graph defined by the following matrix: 0 4 -2] 6 2 3 -3 2 0 4 ∞o 5 0 Show the intermediate matrices after each iteration of the outermost loop.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?
- 2. Consider the graph given by the following adjacency list: vertex adjacent vertics 1 2, 3, 4 2 1 3 1, 4 4 1, 3 5 - (a) Draw the corresponding graph. (b) Write down the adjacency matrix A for this graph. Calculate A2. What is the meaning of the entries of matrices A and A2? (c) Starting at vertex 4, use the adjacency matrix algorithm to check for connectivity. Please no plagiarism and also i want clear hand writting. ThanksRun the Bellman-Ford algorithm for the following graph starting from the node a 3 b a 7 d GProblem 3 1) Consider that you have a graph with 8 vertices numbered A to H, and the following edges: (A, B), (A, C), (B, C), (B, D), (C, D), (C, E), (D, E), (D, F), (E, G), (F, G), (F, H), (G, H) a) Using depth-first search algorithm, what would be the sequence of visited nodes starting at A (show the content of the stack at some steps). b) Same question if the algorithm used in breadth first search. c) What would be the minimum spanning tree rooted at A if a Depth First Search algorithm is used (refer to question a), show few steps in running the algorithm. d) What would be the minimum spanning tree if a Breadth First Search algorithm is used (refer to question b), show few steps of the algorithm.
- Please help me solve this problema. Show that K6.7 has a path containing all vertices in the graph. b. Explain why K6,7 is not Hamiltonian.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.
- [Problem 10] Run the Dijkstra's algorithm on the following directed graph and find all shortest paths between vertex A and all others. B A 7 4 1 D E FUse the best algorithm to find Hamilton circuit with the graph list the circuit beginning at vertex D. 3. Given the graph below. Illustrate Dijkstra algorithm to find the shortest path from vertex s as the source. G 10 15 2 2 5 d