Minimal right determiners of irreducible morphisms in string algebras

Let $\mathrm{\Lambda }$ be a finite dimensional string algebra over a field with the quiver $Q$ such that the underlying graph of $Q$ is a tree, and let $\mathrm{\mid }\text{Det}(\mathrm{\Lambda })\mathrm{\mid }$ be the number of the minimal right determiners of all irreducible morphisms between indecomposable left $\mathrm{\Lambda }$-modules. Then we have $$\mathrm{\mid }\text{Det}(\mathrm{\Lambda })\mathrm{\mid }=2n-p-q-1,$$ where $n$ is the number of vertices in $Q$, $p=\mathrm{\mid }\{i\mid i$ is a source in $Q$ with two neighbours$\}\mathrm{\mid }$ and $q$ is the number of non-zero vertex ideals of $\mathrm{\Lambda }$.