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- Traversing a graph using DFS or BFS traversal on the same staring vertex s, results in a spanning tree T distinguished by discovery edges. What is the main difference between the spanning tree generated by DFS compared to the BFS tree?9. Find the minimum spanning tree of the graph in the Figure below the Figure attached with messageFor a graph with 10 nodes, the minimum spanning tree should have ___ edges. Question 3 options: 10 9 8 11
- Design an algorithm for finding a maximum spanning tree (a spanning tree with the largest possible edge weight) of a weighted connected graph. OR Write the algorithm for maximum spanning tree.Draw and list the edges of a minimum spanning tree for the following graph in theorder that they are added by Kruskal’s algorithms. Show the Set S and the set A in the order thatthe edges are added. Draw the final MST.2. Consider the graph G2(V2, E2) below. 2a. Find the MST of this graph with Kruskal’s algorithm. Draw the MST, and show the table [edge] [w(u, v)] [mark]. 2b. Find the MST of this graph with Prim’s algorithm starting at vertex 'a'. Draw the MST and list the vertices in order you added them to the MST. 2c. Would you get a different MST if you repeat 2b starting at vertex 'e'? Why or why not?
- Consider flight network having places of departure and destination. Flight network represent Page 4 of 4place name as a node and flight trajectories between palce names are the edges. ConsiderPakistan cities as a node and show the source and destination paths, show all the paths separatelywith their labels and include their code as well.Analyze this scenerio that tree or graph should implement here, justify and also implement thiswith appropiate data structure.Example:Network represents that there are three cities named Karachi, Islamabad and Lahore. Flightschedule from Karachi to Islamabad, Islamabad to Lahore and Lahore to Karchi. Places save asclass having departure time and day also.Note: You are not allowed to use any built-in Data Structure classes to implement abovescenario1 A spanning tree for an undirected graph is a sub-graph which includes all vertices but has no cycles. There can be several spanning trees for a graph. A weighted undirected graph can have several spanning trees One of the spanning trees has smallest sum of all the weights associated with the edges. This tree is called minimum spanning tree (MST). Find the MST in the following graph using Kruskal?s Algorithm. V={a, b, c, d, e, f, g, h, i, j} and E={(a, b, 12), (a, b, 3), (a, j, 13), (b, c, 12), (b, d, 2), (b, h, 4), (b, i, 25), (c, d, 7), (c, j, 5), (e, f, 11), (e, j, 9), (f, g, 15), (f, h, 14), (g, h, 6), (h, d, 20), (h, i, 1) }. Note: Numeric value is the weight of the corresponding edge.12- A Graph consists of four vertices A, B, C and D. If we start from A, which vertex will be visited first of all by breadth-first search (BFS) algorithm? A C D B
- Consider a weighted graph in which all the weights on the edges are distinct. Suppose that e is the edge with the largest weight. What is the property that the graph must have in order for e to be in the minimum spanning tree? Question options: 1) The graph must be a tree. 2) The edge e must be incident to a vertex of degree 1. 3) The weight of e must be close to the next largest weight. 4) The graph is no longer connected if e is removed.Which of the following best states the property of a spanning tree of a graph M? 1. It is always acyclic.2. It does not include each vertex of the graph M. 3. It is not a subgraph of M. 4. The graph M has only one spanning tree.9) Given the following graph and the source node F (the 1st node to be discovered), which of the following could be the 3rd node to be discovered during a DFS? A. A B. E C. B D. J E. All