There are only 3 possible edges. The graphs are

1. A triangle, where all 3 edges are present;
2. A v, where just two edges are present;
3. A graph where there is just one edge, leaving the third vertex isolated;
4. A graph with no vertices.

For 3-vertex graphs, all that matters is the number of edges. That is not so for n-vertex graphs where n > 3. Can you think of two nonisomorphic graphs with 4 vertices and two edges?