LetG= (V, E) be a graph. A vertex cover inGis a subset of verticesS, so thatfor every edge e= ab∈E, either a∈Sor b∈S. Now T= (V, E) be a tree with non-negative weights assigned to its vertices. Describe a linear time algorithm for computing a vertex cover of minimum weight. (Weight of a vertex cover is sum of vertex weightsinit.)You should define all necessary terms in your proposed solution, and clearly outline your algorithm.

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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.