Definition:Rooted Tree/Descendant

Definition

Let $T$ be a rooted tree with root $r_T$.

Let $t$ be a node of $T$.

A descendant node $s$ of a $t$ is a node such that $t$ is in the path from $s$ to $r_T$.

That is, the descendant nodes of $t$ are all the nodes of $T$ of which $t$ is an ancestor node.

Proper Descendant

A proper descendant node of $t$ is a descendant of $t$ which is not $t$ itself.

Also see

• Results about descendant nodes can be found here.

Sources

• 1979: John E. Hopcroft and Jeffrey D. Ullman: Introduction to Automata Theory, Languages, and Computation ... (previous) ... (next): Chapter $1$: Preliminaries: $1.2$ Graphs and Trees: Trees