Definition:Extension of Rooted Tree

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Definition

Let $\left({T, r_T}\right)$ and $\left({S, r_S}\right)$ be rooted trees.


Then $\left({S, r_S}\right)$ is an extension of $T$ if and only if:

$T$ is a subtree of $S$;
$r_S = r_T$.

That is, if and only if $T$ is a rooted subtree of $S$.



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