This question was previously asked in

GATE CS 2012 Official Paper

Option 4 : None of the above

The correct answer is **“option 4”.**

__CONCEPT:__

A **spanning tree** of graph G is a subset of G which has all vertices covered with the minimum possible number of edges.

Some **properties** of spanning tree are:

1. Spanning tree **doesn’t contain any cycle**.

2. Spanning tree** cannot be disconnected**.

Every connected and undirected graph G has at least** one spanning tree.**

__EXPLANATION:__

Consider graph **G** with edge weights > 1,

Consider graph **G’ **with squared edge weights of graph G,

The minimum spanning tree **(T)** of graph G is:

Minimum Spanning Tree **(T’)** of graph G’ is:

So, **T is not equal to T'and t' < t ^{2}.**

**Hence, the correct answer is "option 4".**