Assume you have been given a graph with 1 minimum spanning tree and no repeated edge weights. Using the min-cut theorem, prove Boruvka's algorithm is correct. The pseudocode is attached.

Q: Show that the maximum number of edges in a simple graph with n vertices is n(n-1)/2.

A: Introduction :Given , A simple graph , number of vertices = n We have to show that maximum number of…

Q: Use Prim's algorithms AND the Kruskal's algorithm to find the minimum spanning tree for the given…

A: below is the minimal spanning tree using given algorithms

Q: For the following graph, list the vertices in the order they might be encountered in a breadth first…

A: Given: For the following graph, list the vertices in the order they might be encountered in a…

Q: How many spanning trees does the following graph have?

A:

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Q: 4.73. Does Prim's algorithm always give the same minimum weight spanning tree as Kruskal's…

A: Yes, prism's algorithm give the same minimum weight spanning tree as kruskal's algorithm when all…

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A: The question asks to calculate the total number of edges where one graph is a complete graph with 5…

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Q: Dijkstra's shortest path algorithm is run on the graph, starting at vertex D. Each row in the table…

A: The answer as given below:

Q: it step by step. Answer: here a 5 b 6 3 1 d 4 2 6

A: Spanning Tree : - A spanning tree for a graph is a subgraph that includes every vertex of the…

Q: Suppose we have a graph as follows A) Show the order of visit for the vertices using Depth First…

A: Below are the answers of BFS and DFS:

Q: Given a complete graph with 5 nodes, and different weights of the edges, how do you find the minimum…

A: answer is

Depth First Search

Depth-first search (DFS) also known as Depth First traversal is an algorithm used to traverse or search the nodes in a tree or graph data structure. Traversal usually means visiting all the nodes of a graph. DFS performs in a depth-ward manner. It uses a stack to remember the vertices it has visited. The search starts from the root node, where any arbitrary node is selected as a root node in a graph, and then each node is explored along each branch before performing backtracking. The DFS algorithm uses a recursive technique by following the idea of backtracking. DFS algorithm does this by performing an in-depth search of all the nodes by traversing in a forward direction. If the required node is not found, it starts backtracking to previously visited nodes.