mst non distinct

Question

G = (V, E ) is an undirected simple graph and e is a particular edge of G. Which of the following statements about the minimum spanning trees (MSTs) of G is/are TRUE?
I. If e is the lightest edge of some cycle in G, then every MST of G includes e
II. If e is the heaviest edge of some cycle in G, then every MST of G excludes e
(A) I only (B) II only (C) both I and II (D) neither I nor II

Comments

@Srestha

But it is not given distinct edge weight like previous year gate question

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chk the question of GATE

https://gateoverflow.in/39727/gate-2016-1-40

I have one doubt in this question

It is telling about lightest weight

but, in the graph given 3 is lighter than 4

lightest weight is 1

which cannot be eleminated

So, how option 1 is false?

Can u tell me plz

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That question says each edge weight are distinct but this question don't as simple as that

Answer 1

Answer will be D

Here it is not given that all edge weight are different so it is possible for an light edge to be not part of MST ( in such case the light edge must be part of cycle of same edge weight)

It is possible for heaviest weight edge to be part of MST such edge would be either bridge of pendent edge

Comments

chk the question of GATE

https://gateoverflow.in/39727/gate-2016-1-40

I have one doubt in this question

It is telling about lightest weight

but, in the graph given 3 is lighter than 4

lightest weight is 1

which cannot be eleminated

So, how option 1 is false?

Can u tell me plz