in our course we had to draw all non-isomorph graphs with 7 knots without loops. Since this is hard to explain I'll add an Image.
The blue written part is accepted by the tutor and the pencil written part is what I think should be included. I'm not sure if the tutor forgot to include those or if there is a reason why not since they seem to have a different structre than all the above.
In case the picture is hard to read here I uploaded it somewhere else too: http://img5.fotos-hochladen.net/uploads/isomorphgraph0a2tmsufqb.jpg
Edit: It has been suggested that the correct way to put it was
"I think the English phrasing would be to draw all non-isomorphic trees on seven vertices"
Thanks!
The intuition is that two graphs are isomorphic if one can redraw one to get the other.
In your case, your left-most graph is isomorphic to graph $1$, since you could "straighten" that horizontal edge to a vertical edge to get graph $1$. Similarly, your middle graph is isomorphic to graph $3$ and your right-most graph is also isomorphic to graph $3$ (turn it upside down).