What does a topological sort return for a directed acyclic graph?

A topological sort returns a linear ordering of the vertices in a directed acyclic graph (DAG) such that for every directed edge from vertex A to vertex B, vertex A comes before vertex B in the ordering. This characteristic makes topological sorting particularly useful in scenarios where there are dependencies between tasks or events, as it respects these dependencies.

In a DAG, since there are no cycles, it's always possible to arrange the vertices linearly based on their dependencies. Each vertex can be processed once all its prerequisite vertices (those that point to it) have been processed, ensuring that the directed relationships are maintained throughout the ordering. The resulting linear order reflects a valid sequence in which tasks can be performed, making it applicable in various fields, such as scheduling, course prerequisite ordering in education, and resolving symbol dependencies in linkers.

The other options do not accurately reflect the nature of a topological sort. A random ordering of vertices would not provide any meaningful structure and ignore the dependencies inherent in a DAG. A complete graph of vertices refers to a graph where every pair of distinct vertices is connected by a unique edge, which does not apply to the context of topological sorts. A set of disconnected components implies an absence of order or relationships, which contradicts