TADM2E 6.3

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No. Counter example provided below:

G(V,E,W) = ((A,B,C,D),({A,B},{B,C},{C,D},{D,A}),(1,2,3,4))

Minimum spanning tree has a weight of 6 with edges {A,B},{B,C},{C,D}.

In the full graph the minimum distance between A and D is 4.