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Q) Given a network with nodes and arcs , we say that two nodesare \" adjacent \"

ID: 3611044 • Letter: Q

Question

Q) Given a network with nodes and arcs , we say that two nodesare " adjacent " if there is an arc between them. ( we don't carewhich direction the arc is pointing ; either way is okay.) A cliquein a network is a set of nodes that are all adjacent to each other.An independent set in a network is a set of nodes where none areadjacent to any other. correctly answering the question " does this network contain aclique of K nodes ? " is np- complete. Demonstrate that correctlyanswering the question " Does this network contain an independentset of K nodes ? " is also NP- Complete. Q) Given a network with nodes and arcs , we say that two nodesare " adjacent " if there is an arc between them. ( we don't carewhich direction the arc is pointing ; either way is okay.) A cliquein a network is a set of nodes that are all adjacent to each other.An independent set in a network is a set of nodes where none areadjacent to any other. correctly answering the question " does this network contain aclique of K nodes ? " is np- complete. Demonstrate that correctlyanswering the question " Does this network contain an independentset of K nodes ? " is also NP- Complete.

Explanation / Answer

Dear,

   An independent set in a network is a set of nodeswhere none are adjacent to any other: In an undirected graph, asubgraph wherein each node is connected to each other node in thesubgraph is a clique. Give an integer k and a graph, theproblem is to determine there is a clique of size k anywhere in thegraph. A clique of size k is called a k-clique

It is simple to find a verifier for CLIQUE, using the nodes inthe clique as the certificate:

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