Definition:Rooted Tree/Ancestor Node

Definition

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

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

An ancestor node of $t$ is a node in the path from $t$ to $r_T$.

Proper Ancestor

A proper ancestor node of $t$ is an ancestor node of $t$ that is not $t$ itself.

Also see

• Path in Tree is Unique: the path from $t$ to $r_T$ is indeed unique.

• Results about ancestor 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
• 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.7$: Tableaus