FIGURE 3 A Weighted Simple Graph. What is the length of a shortest path between a and z in the weighted graph shown in Figure 3?
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- Given the following Graphs: Graph A: В 12c 1 4. E F G- H 4 J K 3 Graph B: Graph B is the undirected version of Graph A. 3.50 D A 40 100 20 30 50 160 C 300 150 400 B F H 150 220 250 500 G 200 Figure 3: A weighted undirected Graph for Question 9 and 10 10. For the graph as shown in Figure 3, find the minimum spanning tree based on Kruskal's Algorithm. Show the detailed steps of your calculation.An undirected weighted graph G is given below: Figure 16: An undirected weighted graph has 6 vertices, a through f, and 9 edges. Vertex d is on the left. Vertex f is above and to the right of vertex d. Vertex e is below and to the right of vertex f, but above vertex d. Vertex c is below and to the right of vertex e. Vertex a is above vertex e and to the right of vertex c. Vertex b is below and to the right of vertex a, but above vertex c. The edges between the vertices and their weight are as follows: d and f, 1; d and e, 4; f and e, 2; e and a, 2; f and a, 3; e and c, 5; c and a, 7; c and b, 5; and a and b, 6.(a) Use Prim’s algorithm to compute the minimum spanning tree for the weighted graph. Start the algorithm at vertex a. Show the order in which the edges are added to the tree.(b) What is the minimum weight spanning tree for the weighted graph in the previous question subject to the condition that edge {d, e} is in the spanning tree?(c) How would you generalize this idea? Suppose…
- Suppose a graph has 6 vertices of degree two, 12 vertices of degree three, and k vertices of degree 1. If the graph has 71 edges, then the value of k isAn undirected weighted graph G is given below Figure 16: An undirected weighted graph has 6 vertices, a through f, and 9 edges. Vertex d is on the left. Vertex f is above and to the right of vertex d. Vertex e is below and to the right of vertex f, but above vertex d. Vertex c is below and to the right of vertex e. Vertex a is above vertex e and to the right of vertex c. Vertex b is below and to the right of vertex a, but above vertex c. The edges between the vertices and their weight are as follows: d and f, 1; d and e, 4; f and e, 2; e and a, 2; f and a, 3; e and c, 5; c and a, 7; c and b, 5; and a and b, 6. (a) What is the minimum weight spanning tree for the weighted graph subject to the condition that edge {d, e} is in the spanning tree? (b) How would you generalize this idea? Suppose you are given a graph G and a particular edge {u, v} in the graph. How would you alter Prim’s algorithm to find the minimum spanning tree subject to the condition that {u, v} is in the tree?In the given weighted graph, find the shortest path from A to E using Dijkstra's algorithm. Please describe the sequence of steps. At the end, your answer should clearly indicate which is the shortest path that you found, and its length. You should also give the final labels on each of the vertices. B 9. E 10 D A 2 3 F 3 G
- Run the Dijkstra's algorithm on the following graph and find all shortest paths between vertex A and all others. B 2 A 6 8 5 C 4 3 6 D 9 E F 10 1 5Consider the graph G : B D E F ASuppose you have a graph G with 6 vertices and 7 edges, and you are given the following information: The degree of vertex 1 is 3. The degree of vertex 2 is 4. The degree of vertex 3 is 2. The degree of vertex 4 is 3. The degree of vertex 5 is 2. The degree of vertex 6 is 2. What is the minimum possible number of cycles in the graph G?
- Consider the following undirected weighted graph: 6 a A. 24 B. 23 C. 15 D. 19 b 2 4 f 7 4 10 d 7 (1) What is the weight of the MST using Kruskal's Algorithm? (2) Please draw the graph of the MST generated by using Kruskal's Algorithm.Additional Topics: Hamiltonian Paths and Cycles A Hamiltonian path in a directed graph is a path that visits every vertex in the graph exactly once. A Hamiltonian cycle in a directed graph is a cycle that visits every vertex in the graph exactly once (except for the vertex at the beginning and end of the cycle). For example, in the following directed graph, 1,3,4,2 is a Hamiltonian path and 1,3,4,2, 1 is a Hamiltonian cycle. 2 3 4 7. Given the following directed graphs: 田街 G1 Answer the following questions: G2 Is there a Hamiltonian path in the graph? If so, find one. • Is there a Hamiltonian cycle in the graph? If so, find one. G3Given the following example of UAG graphs: i)- In Java, give implementation to find the shortest path for graph 1 2 12 9 10 3 5 \21 14 15 8. 4