Which one is right ? Graph theory

Question

1. whenever cut edges exist, cut vertices also exist because at least one vertex of a cut edge is a cut vertex.
2.  if a cut vertex exists, then a cut edge may or may not exist.

Comments

Cut edges imply Cut vertices. But

Cut vertex existence does not guarantee cut edge existence.

Ex: 

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2 vertex are connected to each other, In this graph cut egde is exist but cut vertex is not exist

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@Urvesh i think if n>2 then  this statement is correct

 

Answer 1

you can check this.