Several Subgraphs Connected Components Exam Practice

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For each of the following subproblems, briefly explain how you would solve each. You do not need to write pseudocode. Give a big-O estimate on your solution with a very brief justification.

Given a graph G=(V,E) with n nodes and m edges, determine the number of connected components in G.

Given a connected graph G=(V,E) with n nodes and m edges, determine whether it is possible to color all of the nodes in V either blue or gold such that if (v,w)∈E, then v and w do not have the same color.

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Explanation & Answer

View attached explanation and answer. Let me know if you have any questions.I have tried my best to explain everything in a simple manner. Feel free to ask anything you could not understand. Thanks and Regards.

Q1. What is a connected component? A graph is made up of several subgraphs (these
subgraphs are called connected components). In a connected component you can reach any
other vertices by traversing the edges.
Suppose there is a graph of n = 5 nodes and edges in it are as follows:
Here If you will see this is how your graph will look like :

Here you can see that this graph is made up of two different connected components denoted by
{2, 3, 5} and {1, 4}.
You can see that you can traverse from any node to any other node but that should lie...

Really great stuff, couldn't ask for more.


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