Graph Theory - Can a tree be made of just one vertex?

Question

The question is very simple.

Can a tree be made of just 1 vertex?

Thank you for your help.

Answer 1

Recall the definition of a tree: A connected graph with no cycles.

The graph with one vertex and no edges is connected: For every pair of vertices (there is only one such pair) there is a path from one to the other (just stay where you are)

The graph with one vertex and no edges has no cycles: A cycle must have at least three vertices.

Answer 2

Of course, the number of edges is $0$ and the number of vertices is $1$ and has no cycle. Notice that equation $$|E| = |V|-1$$ is still satisfied since this graph is connected.