Question

Consider the following statements regarding simple undirected graphs
I. If a graph G with n vertices has n - 1 edges, then G is a tree.
II. If a graph G with n vertices is acyclic then G is a tree.

Which of the above statements are correct?

• A. Only II
• B. Both I and II
• C. Only I
• D. None of these

Answer 1

The correct option is D None of these

Both are false.

I is false. Here's a graph has 4 vertices and 3 edges, and yet it is not a tree because it is not connected.



II is false because even though G is acyclic, G may be disconnected. So II is also false.