Pre-topological order

In the field of computer science, a pre-topological order or pre-topological ordering of a directed graph is a linear ordering of its vertices such that if there is a directed path from vertex u to vertex v and v comes before u in the ordering, then there is also a directed path from vertex v to vertex u.[1][2]

If the graph is a directed acyclic graph (DAG), topological orderings are pre-topological orderings and vice versa.[1] In other cases, any pre-topological ordering gives a partial order.

References
  1. Schrijver, Alexander (2002-12-10). Combinatorial Optimization: Polyhedra and Efficiency. Springer Science & Business Media. p. 89. ISBN 9783540443896.
  2. Sedgewick, Robert; Wayne, Kevin (2016-09-26). "Directed Graphs". Algorithms, 4th Edition. Retrieved 2017-09-06.
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