Let $G=\left ( V,E \right )$ be $any$ connected, undirected, edge-weighted…

PYQ GATE 2017

Let $G=\left ( V,E \right )$ 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 of the above statements is/are necessarily true?

A.
I only
B.
II only
C.
both I and II
D.
neither I nor II

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Let \(G=\left ( V,E \right )\) be \(any\) connected, undirected, edge-weighted…