Which property is necessary for a simple graph to be a tree?
It must contain a cycle.
It must have ∣E∣=∣V∣+1|E| = |V| + 1∣E∣=∣V∣+1.
It must be connected and ∣E∣=∣V∣−1|E| = |V| - 1∣E∣=∣V∣−1.
Every vertex must have degree at least 2.