Formally, the 3 graphs are isomorphic because there is a mapping of labels that would make them equal. For example, Graph #1 is isomorphic with Graph #3 using the following mapping:
| Graph #1 label | Graph #3 label |
| A | B |
| B | A |
| C | C |
| D | D |
In words, if you flip A and B in graph #3, you get graph #1.
Graphs #1 and #3 are obviously different. What might not be so obvious is that graph #1 and graph #2 are the same. Although graphs #1 and #2 may look different, you can see that they're really the same. They're just drawn differently. For example, here's an adjacency matrix representation of both graphs:
| Vertex | has edges to these vertices |
| A | B,C |
| B | (nothing) |
| C | (nothing) |
| D | B,C |
So, basically, A and D both still go to B and C, even if we choose to draw B and C in different places.
Graph #3 is different from graphs #1 and #2, since the labels don't arrow each other in the same way. Here's the adjacency matrix of graph #3:
| Vertex | has edges to these vertices |
| A | (nothing) |
| B | A,C |
| C | (nothing) |
| D | A,C |