What type of tree is this? 
The checkmarks I've drawn means that the branch ends or a node with the same number allready exists in the tree. I.e it means it reaches some cycle or ends the branching.
I don't know if this is even called a tree? But if so, what kind of specific tree is it? I would like to study this more, but don't know where to find literature on the specifics of this. (This tree has nodes with actual binary values but I used decimal for better visualization).
And also there are two "roots". But some of the nodes could have been connected, like node: 10, but I don't want to clutter the structure too much, or maybe I should redraw the tree-structure altogheter?
Updated: I've improved the nodes. Now it looks more like a graph. So the question is now is it a digraph and/or what can I derive from this?

 A: Assuming I understand what you have tried to show in your second image, you have
a directed graph (digraph) with a loop and nodes of outdegree two. There may be other structure that you can endow your digraph with if you need it. You don't have a tree because there are directed cycles, for example, $\ 4 \to 10 \to 4. \ $ You can try to find spanning trees of the digraph if you need it. You can try to  use it as the basis for a nondeterministic finite automaton.
Your first image seems to be a labeled multi-rooted tree representing the
walks from the two root
nodes (12 and 4) in the labeled digraph in your second image. You asked

So the question is now is it a digraph and/or what can I derive from this?

and the answer is "yes". The multi-rooted tree is one graph object
associated with your digraph.
A: I can not fully understand what do the brach ends mean. But if we will ignore them, then we will get a forest, which includes two binary trees. These trees are called binary because each node has two children (and a binary tree is a tree in which each node has at most two children). I don't think you can say anything interesting about the two trees besides the fact that they are binary.
The definitions of tree and forest:

Tree - an undirected graph in which any two vertices are connected by exactly one path.
  Another definition: Connected graph without cycles.  
Forest - graph without cycles. 

(I am sorry for the English, I know it is not perfect)
