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- Find the minimum cost spanning tree on the graph above using Kruskal's algorithm. Which of the edges below are included in the minimum cost tree? PLEASE HELP[This is multiple choice#3and4] 3) In the given figure, using Kruskal’s algorithm, which edge should we choose last?a. BCb. ABc. ACd. CDe. None of the above 4) In the given figure, which of the following edges of the given graph are not part of the minimum spanning tree?a. ACb. EFc. AGd. BGe. None of the above12- 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
- Please help... Adding one more vertices... highlighted with with bold... Let A, B, C, D be the vertices of a square with side length 100. If we want to create a minimum-weight spanning tree to connect these four vertices, clearly this spanning tree would have total weight 300 (e.g. we can connect AB, BC, and CD). But what if we are able to add extra vertices inside the square, and use these additional vertices in constructing our spanning tree? Would the minimum-weight spanning tree have total weight less than 300? And if so, where should these additional vertices be placed to minimize the total weight? Let G be a graph with the vertices A, B, C, D, and possibly one or more additional vertices that can be placed anywhere you want on the (two-dimensional) plane containing the four vertices of the square. Determine the smallest total weight for the minimum-weightIf a minimum spanning tree has edges with values 41, 13, 32 and 39, then what is the length of the minimum spanning tree?a) What is Minimum Spanning Tree. b) State the number of edges in a minimum spanning tree of a network with10vertices. c) State the number of edges in a minimum spanning tree of a network withnver tices.
- ID - 1542553 Problem 2Consider the graph from Problem 1 (Figure 1).The goal is to find single source shortest paths (in particular, the Shortest Paths Tree) starting from source node s (see Weights and Source Node in picture). (i) Find the Shortest Paths Tree (SPT) in G starting with source vertex s using Dijkstra’s algorithm. Show the main steps of the algorithm. Note that the graph has a negative weight edge. Does Dijkstra’s algorithm still find the correct shortestpaths? (ii) Find the Shortest Paths Tree (SPT) in G starting with source vertex s using Bellman-Ford’s algorithm. Show the main steps of the algorithm. (iii) Suppose we want to the shortest path distances between all pairs of nodes such that the shortest paths use intermediate vertices only from the set {a, b, g}. Use the Floyd-Warshall algorithm to compute these distances between all pairs of nodes.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 abovescenarioLet A, B, C, D be the vertices of a square with side length 100. If we want to create a minimum-weight spanning tree to connect these four vertices, clearly this spanning tree would have total weight 300 (e.g. we can connect AB, BC, and CD). But what if we are able to add extra vertices inside the square, and use these additional vertices in constructing our spanning tree? Would the minimum-weight spanning tree have total weight less than 300? And if so, where should these additional vertices be placed to minimize the total weight? Let G be a graph with the vertices A, B, C, D, and possibly one or more additional vertices that can be placed anywhere you want on the (two-dimensional) plane containing the four vertices of the square. Determine the smallest total weight for the minimum-weight spanning tree of G. Round your answer to the nearest integer. Note: I encourage you to add n additional points (for n=1, 2, 3) to your graph and see if you can figure out where these point(s) need to…
- Let A, B, C, D be the vertices of a square with side length 100. If we want to create a minimum-weight spanning tree to connect these four vertices, clearly this spanning tree would have total weight 300 (e.g. we can connect AB, BC, and CD). But what if we are able to add extra vertices inside the square, and use these additional vertices in constructing our spanning tree? Would the minimum-weight spanning tree have total weight less than 300? And if so, where should these additional vertices be placed to minimize the total weight? Let G be a graph with the vertices A, B, C, D, and possibly one or more additional vertices that can be placed anywhere you want on the (two-dimensional) plane containing the four vertices of the square. Determine the smallest total weight for the minimum-weight spanning tree of G. Round your answer to the nearest integer. Attention: Please don't just copy these two following answers, which are not correct at all. Thank you.…Please show step-by-step explanations. Thank you. About the Petersen Graph, (a) The Petersen Graph P is shown below. Assign an edge weight of 1 to each edge of P. Use either Kruskal or Prim’s Algorithm to find a (necessarily minimum weight)spanning-tree of P. you must be clear about whichthe algorithm you choose and show and explain each step leading to the spanning tree.modify this code to find the required output; graph={ 1: [2,3], 2: [1,3], 3: [1,2,5, 4], 4: [6,11,3,5], 5: [7,4,3], 6: [8,4], 7: [5,9], 8: [6], 9: [7,10], 10: [9,12], 11: [12,4], 12: [10,11] } #perform depth-first search def dfs(graph, start, visited, charge): #current node as visited visited.add(start) #Check the Roomba needs to enter the charging station if charge <= 6: print(f" {start} (Charging, {charge} Wh) -> ") charge =12 else: print(f"{start} (Cleaning, {charge} Wh) ->") charge -= 1 #Take he list of adjacent nodes adj_nodes = graph[start] #Visit the unvisited adjacent nodes for node in adj_nodes: if node not in visited: dfs(graph, node, visited, charge) #user to enter the starting node start_node = int(input ("Enter starting node: ")) # Perform depth-first search starting from the starting node visited = set() dfs(graph, start_node, visited, 12) # Sample outputEnter starting node: 11 (Cleaning, 12 Wh) ->2…