acyklic

Acyclic, also seen as acyklic in some languages, is an adjective describing the absence of cycles in a structure. The term is used across disciplines, where a cycle is a closed path or loop that returns to its starting point. In general, acyclic means that a structure cannot form or sustain a closed loop.

In graph theory, an acyclic graph contains no cycles. Undirected acyclic graphs are forests; a connected acyclic graph is a tree. Directed acyclic graphs (DAGs) have no directed cycles and admit a topological ordering, which supports scheduling, dependency analysis, and data processing pipelines.

In chemistry, an acyclic compound lacks ring structures; its atoms form open chains rather than closed rings. Acyclic hydrocarbons include alkanes, alkenes, and alkynes not contained within rings. Acyclic molecules can be linear or branched.

In topology and homological algebra, an acyclic space or chain complex has trivial reduced homology groups, meaning there are no nontrivial cycles surviving homology. Acyclicity does not imply contractibility in general.

Etymology and usage: the term derives from Greek a- meaning “not” and kyklos meaning “circle.” The concept is often contrasted with cyclic or ring-containing structures, and it is applied in mathematics, computer science, chemistry, and related fields.