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

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,)vi, j en,i + j}! All edges have a weight w(v,v)=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 vand v. ii. The weight sum between all pairs of vertices is the sum of all weight sums s(vi,v;) for all i,j and itj or s= s(v;V;) i=1 j=1, jui a) Vi 1+1 Wn

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