Definition:Tree (Graph Theory)

Context
Graph Theory

Definition
A tree is a simple connected graph with no circuits:



Equivalently, it can be defined as a simple connected graph with no cycles.

Node
The vertices of a tree are called its nodes.

Simple properties

 * All trees are bipartite, from Bipartite Graph has No Odd Cycles (as a tree has no cycles at all).


 * No (non-edgeless) tree is Eulerian, as it has no circuits, let alone Eulerian ones.

Note
In some contexts, the term tree is used to mean rooted tree.