Let $Γ^{(x_0)}$ be a finite rooted tree, for which $Γ$ is the underlying tree and $x_0$ the root. Let $T$ be the Terwilliger algebra of $Γ$ with respect to $x_0$. We study the structure of the principal $T$-module. As a result, it is shown that $T$ recognizes the isomorphism class of $Γ^{(x_0)}$.
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