Acyclic

Definition

Acyclic refers to a graph that contains no cycles. In other words, it is a graph where there is no way to start at one vertex and return to it by following the edges.

5 Must Know Facts For Your Next Test

1. An acyclic graph does not contain any closed loops.
2. All trees are acyclic graphs.
3. In an acyclic graph, the number of edges is always less than the number of vertices.
4. A directed acyclic graph (DAG) has directed edges and no cycles.
5. Acyclicity can be checked using algorithms like Depth-First Search (DFS).

Review Questions

• What does it mean for a graph to be acyclic?
• Why are all trees considered acyclic?
• How can you determine if a graph is acyclic?

Related terms

Cycle:

A path that starts and ends at the same vertex, with all edges distinct.

Tree: A connected acyclic graph.

Directed Acyclic Graph (DAG): A directed graph with no directed cycles.