MAT115 Tree Terminology

NB: in the tree world, we'll frequently use the word "node" rather than "vertex". They're synonyms, after all, but it's one syllable instead of two, and mathematicians are notoriously lazy!:)

• tree: an acyclic, connected graph with one specially designated vertex (or "node") called the root node.

  "Acyclic" means that there are no cycles.

  

• parent node: the node adjacent to a given node on the path to the root node

  Node 2 is the parent of nodes 6 and 7.

• child node: a node adjacent to a node (its parent) which is closer to the root node

  Nodes 6 and 7 are the children of node 2.

• siblings: nodes sharing the same parent.

  Nodes 6 and 7 are siblings.

• internal node: a node with a child

  Node 2 is internal, as a parent.

• leaf node: a childless node

  Node 6 is a leaf.

• depth of a node: the length of the path from the node to the root

  Node 6 is at depth 2.

• depth (or height!) of the tree: the maximum node depth

  This tree has depth 3.

• binary tree: a tree in which a root node has at most two children but no parent, each internal node has a single parent and at most two children, and leaf nodes have a single parent but no children.

  This tree is not binary; it's called "ternary", because parents have at most three children!

  Here's a binary tree:

  

• left child: the node to the left of the parent in a binary tree
• right child: the node to the right of the parent in a binary tree
• perfect binary tree : all leaf nodes are of equal depth, and all parents have two children:
  

• complete binary tree: an almost-full binary tree (all leaves are of depth n or n-1, where n is the depth of the tree).

• forest: a bunch of trees (of course! Geez, ask a silly question....)