Let G V E be any connected undirected edge weighted graph The weights of the edges in E are positive any distinct Consider the following statements gate computer science 2017

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## Let G = (V, E) be any connected undirected edge-weighted graph. The weights of the edges in E are positive any distinct. Consider the following statements: -gate computer science 2017

I. Minimum Spanning Tree of G is always unique.
II. Shortest path between any two vertices of G is always unique.

Which of the above statements is/are necessarily true ?

A) I only
B) II only
C) both I and II
D) neither I and II
A) I only

Explanation:
I. Minimum Spanning Tree of G is always unique - MST will wlways be distinct if the edges are unique so Correct II. Shortest path between any two vertices of G is always unique - Shortest path between any two vertices can be same so incorrect Therefore, option A is correct .

This explanation is contributed by Deepak Raj.

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