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Let T be a minimum spanning tree of graph G obtained by Prim’s algorithm. Let Gnew...

Let T be a minimum spanning tree of graph G obtained by Prim’s algorithm. Let Gnew be a graph obtained by adding to G a new vertex and some edges, with weights, connecting the new vertex to some vertices in G. Can we construct a minimum spanning tree of Gnew by adding one of the new edges to T ? If you answer yes, explain how; if you answer no, explain why not.

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Answer #1

Considering the above Graph, MST of Gnew is missing with an edge compared to the Graph G. Hence its uses the vertices of both the Graph G and Gnew.

Hence we conclude that this if possible in some cases and not possible in some cases. If we add new edges to Graph T, in some cases it is possible and in some cases it is not possible because it all depends on the weight of new edges which is being added, and in some cases MST of T will differ if the new weight is smaller than the weight in the original graph.

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