Question: Minimum Spanning Trees Consider an undirected graph, G = ( V , E ) , with non - negative edge weights such that w (

Minimum Spanning Trees
Consider an undirected graph, G=(V,E), with non-negative edge weights such that w(e)1,AAeinE. Suppose that you have computed a minimum
spanning tree for G, as well as the shortest paths to all nodes from a particular node sinV. Decrease the weights of all edges in the graph, such that
w'(e)=w(e)-1,AAeinE.
a.(10 pts) Does the MST of G change under this weight adjustment? Either provide an example of a graph for which it does change, or prove that it
cannot change.
b.(10 pts) Do the single-source shortest paths from s change? Either provide an example of a graph for which it does change, or prove that they cannot
change.
Minimum Spanning Trees Consider an undirected

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