# It's a mystree

The minimum spanning tree of the graph is draw on the graph using bold purple lines. As you can see , the weights of edges $$x$$,$$y$$ and $$z$$ are unknown.

The tightest bounds for $$x$$,$$y$$ and $$z$$ can be written as below for some $$p,q,r \in \mathbb{Z}^{+}$$:

$x \geq p$ $y \leq q$ $z \geq r$

What is the value of $$p+q+r$$?