Topological sorting is a linear ordering of vertices in a directed acyclic graph (DAG) such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering. It is crucial for scheduling tasks, organizing data dependencies, and solving problems that require ordering with precedence constraints.

Topological Sorting

Topological sorting

Linear ordering is a binary relation on a set that arranges the elements in a sequence where every pair of elements is comparable, following transitivity, antisymmetry, and totality. This concept is pivotal in mathematics and computer science, enabling the organization of data and facilitating algorithms for sorting and searching.

linear ordering

A Directed Acyclic Graph (DAG) is a finite graph with directed edges and no cycles, meaning there is no way to start at any vertex and return to it by following the directed edges. DAGs are crucial in various fields such as computer science and data processing for representing structures with dependencies, like task scheduling, version control, and data workflows.

directed acyclic graph

directed edge

A vertex is a fundamental element in geometry and graph theory, representing a corner or intersection point where two or more lines, edges, or curves meet. In the context of graphs, a vertex is a node that may connect to other vertices via edges, playing a crucial role in the structure of networks and geometric shapes.

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