You are given a weighted graph G with n nodes and m edges whose weights

are all positive. Let T be a minimum$-$spanning tree of this graph. Answer

the following:

$$ Suppose one adds a new edge e that is not already present in G$.$ How

will you use G$,$ e and T to efficiently compute the new minimum

spanning tree for the graph G with the additonal edge e$?$

$$ Suppose one deletes an edge e in T from the entire graph G$.$ How will

you compute a new minimum spanning tree with the edge e deleted?

Please note that identifying the new minimum spanning tree from scratch

$($without using T $)$ will not be awarded any points.