Acyclic

Acyclic can mean any of the following:

In chemistry, an acyclic compound is a hydrocarbon compound having an open chain (i.e., no rings). See aliphatic.
In graph theory, a graph which does not contain any path passing twice by the same node (i.e., no cycles). See directed acyclic graph.
In mathematics, specifically homological algebra, a chain complex is called acyclic if all of its homology groups are zero, or, equivalently, if it is an exact sequence.