Question 8833 – Minimum-Spanning-Tree

Let G be a weighted graph with edge weights greater than one and G’ be the graph constructed by squaring the weights of edges in G. Let T and T’ be the minimum spanning trees of G and G’, respectively, with total weights t and t’. Which of the following statements is TRUE?

Correct Answer: D

Let graph G be

Then MST for G is,

Now let’s square the weights,

Then MST for G’ is,

So, from above we can see that T is not necessarily equal to T’ and moreover (t¹) < (t²).
So option (D) is correct answer.