GATE | Sudo GATE 2020 Mock I (27 December 2019) | Question 48

Consider the weights 1, 1, 2, 2, 3, 3, 4, 4 to the edges of the graph G and following statements:

I. There is a graph G in which unique minimum weight spanning tree is possible in Graph G.
II. There is a graph G in which multiple minimum weight spanning trees are possible in Graph G.

Which of the following statement(s) is/are correct ?
(A) Only I
(B) Only II
(C) Both I and II
(D) Neither I nor II


Answer: (C)

Explanation: Both statements are correct.

In the weighting on the left, the edges of weights 1 and 2 form the unique min cost spanning tree. In the weighting on the right, the two edges of weight 1 together with the ”bottom” edge of weight 2 together with either of the edges of weight 3 form a min cost spanning tree.

Option (C) is correct.

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