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Question 3: Find the Minimum Spanning Tree for the given graph using Prim's algorithm and write the steps. A 4 2 11 с F 8 7 1 2 E D 6 B 7 4 2 G H 5 9 10 T

PLEASE ANSWER ALL QUESTIONS AND SHOW AND EXPLAIN STEPS THANK YOU. PLEASE I NEED THIS ASAP.

I have to use Prim's algorithm to find a minimum spanning tree in the weighted graph. Can someone help?

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.

Draw the minimum spanning tree for the following graph. Use induction to prove your result is a minimum spanning tree.

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-weight

for the graphWhat edges are selected to obtain the minimum spanning tree? Select one or more than one:

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.

Using the Kruskal’s Algorithm, show the minimum spanning tree representation of the graph.