A graph that has no cycles is called acyclic

Question

BlackTom AI · Accepted Answer

Consider the statement in the question: what does it mean for a graph to be acyclic?
Option 1: 'False' — This would claim that a graph with no cycles is not acyclic. That contradicts the standard definition, since acyclic literally means 'without cycles.' Therefore this option is incorrect.
Option 2: 'True' — By definition, a graph that has no cycles is indeed acyclic. In undirected graphs this means no cycle is present; in directed graphs, the term is often specified as 'acyclic graph' or 'DAG' when appropriate, but the core idea remains that absence of cycles characterizes acyclicity. Hence this option is correct.
In summary, the core distinction hinges on cycles: if there are none, the graph is acyclic; if there is at least one cycle, it is not acyclic. The statement aligns with that fundamental concept, making it the accurate choice.

CMPSC 132 Spring 2025 Module 6.2 Checkpoint

A graph that has no cycles is called acyclic

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