The Feedback Vertex Set problem is defined as follows: Given: a graph G and a positive integer k Question: does G have a set S of at most k vertices such that the subgraph induced by the complement of S is acyclic? In other words, the problem asks whether deleting at most k vertices from a graph makes it acyclic. Assume you found a trusted polynomial-time algorithm, A, for the decision version of the problem. Write a polynomial-time algorithm that uses A to solve the search version. 2. Answer the same question for the Graph Coloring problem.

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Q: 1 . Let ƒ(z) = (z − 2) sin (2+2) (a) Find and classify the zeros of f.

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Q: Solve using Laplace Transform y" - 2y + 2y = 4et; y(0) = 2, y'(0) = -1 Oy=2e^-t + te^-t + 2t^2e^-t…

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Q: ................... X.........

A: According to the guidelines, we have to solve only the first question, rest of the question should…

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.