Characteristics of Finite Tree/Condition 2

Theorem

Let $T$ be a finite simple graph of order $n$.

Then:

$T$ is a finite tree of order $n$ if and only if $T$ has $n - 1$ edges and is connected.

Proof

This is an instance of:

Finite Connected Simple Graph is Tree iff Size is One Less than Order.

$\blacksquare$