(old image at bayimg.com/image/iaeidaacn.jpg just there for the post to still make sense)

Both graphs have a braching factor of 3. Graph A is a "tree". Is there a name for the type of graphs as B? (you can ignore the colours)

ps could somebody please change the link into an image?

**edit**
ok, my bad. Clearly I have not as much knowledge of graphs. I am indeed referring to graph searching, as that is something I have more knowledge of. So I suppose I should have drawn arrows, as the graphs are directed from left to right.

- Is it correct that the first graph is called a tree?
- Then, the second graph was supposed to be analogous to a tree. Only with the childnodes of sibling nodes merged, so that the number of nodes grows at a constant rate (3 in my example, but $n$ in the general case) rather than exponential as is the case in the tree.
- I've drawn a new graph image to illustrate more clearly what I mean. Also left out the left-most single node as I think this is a more general graph.

I hope this clears up my drawings a bit.