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 \(p+q+r\)?

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