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Question

Let G = (V, E) be any connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements:
(I) Minimum spanning tree of G is always unique.
(II) Shortest path between any two vertices of G is always unique.

which is true

Comments

it means,

the shortest distance btw two nodes, have unique path.

make a triangle, name them a,b,c

let the edges, a-b = 2, b-c=3, a-c=5 ===> all edges weights are distinct.

the shortest path btw a and c is not unique due to the paths

1) a-c = 5

2) a-b-c = 5

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Oh right!, I considered distance and not the path. Thanks a lot

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If I convert my answer to comment will it retain ur comments of this answer?