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
- An acyclic graph does not contain any closed loops.
- All trees are acyclic graphs.
- In an acyclic graph, the number of edges is always less than the number of vertices.
- A directed acyclic graph (DAG) has directed edges and no cycles.
- 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?
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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.
