Pre-topological order

From HandWiki

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. 1.0 1.1 Schrijver, Alexander (2002-12-10) (in en). Combinatorial Optimization: Polyhedra and Efficiency. Springer Science & Business Media. pp. 89. ISBN 9783540443896. https://books.google.com/books?id=mqGeSQ6dJycC. 
  2. Sedgewick, Robert; Wayne, Kevin (2016-09-26). "Directed Graphs" (in en). http://algs4.cs.princeton.edu/42digraph/.