oneended
Oneended is a term used in mathematics, often hyphenated as one-ended, to describe certain infinite structures that have a single way to go to infinity. In graph theory, a connected infinite graph is one-ended if, after removing any finite set of vertices, the remaining graph has exactly one infinite component. Informally, there is only one “direction” toward infinity.
In geometric group theory, the term extends to finitely generated groups via their Cayley graphs. The number
A central result related to ends of groups is Stallings’ theorem: if a finitely generated group has
Typical examples help illustrate the spectrum. Finite groups have zero ends; Z and the infinite dihedral group
The concept of one-endedness provides a framework for understanding how a structure behaves at infinity and