Question: Consider a fully connected undirected graph G= with n vertices where V={v.,..., V.,} and E = {elv,,v; Ji, j en,i # j}! All edges have

Consider a fully connected undirected graph G= with n vertices where

Consider a fully connected undirected graph G= with n vertices where V={v.,..., V.,} and E = {elv,,v; Ji, j en,i # j}! All edges have a weight w(vv)=1). a) (9+3=12 pts) Draw an MST that minimizes the weight sum between all pairs of vertices! Calculate the weight sum! b) (9+3=12 pts) Draw an MST that maximizes the weight sum between all pairs of vertices! Calculate the weight sum! Hint: i. The weight sum s(v;v;) between vertices v; and v; is the sum of the weights of the edges forming the path between v; and v;. ii. The weight sum between all pairs of vertices is the sum S of all weight sums s(v;v;) for all i,j and itj or S = s(v;,v,)

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