If A is NP-complete, and A has a polynomial time algorithm, then there is a polynomial time algorithm to find the largest clique in a directed. A clique in a graph G(V, E) is a subset of vertices V’ such that there is an edge (u,v) in E between every two vertices u and v in V’. For example, the four vertices u2, u3,u5, and u6 form the largest clique in the graph below.

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A: Actually, the answer has given below:

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Q: Hall’s

A:

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A: Check the solution of part b below.

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A:

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A:

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A:

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A: ANSWER:-

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A:

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Minimum Spanning Tree

A spanning tree is a sub-graph of a connected, undirected graph. It has all the vertices of a graph with the minimum possible number of edges. If a vertex is skipped, then it will not be a spanning tree. The edges of a spanning tree may or may not have weights.