  Let $\Lambda$ 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
$|\Det(\Lambda)|$ be the number of the minimal right determiners of all
irreducible morphisms between indecomposable left $\Lambda$-modules. Then we
have $$|\Det(\Lambda)|=2n-p-q-1,$$ where $n$ is the number of vertices in $Q$,
$p=|\{i\mid i$ is a source in $Q$ with two neighbours$\}|$ and $q$ is the
number of non-zero vertex ideals of $\Lambda$.
