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If the vertices of a digraph with n vertices can have its vertices numbered from 1 to n such that i > j whenever there is a path from i to j, then such a labeling of its vertices is called sorted labeling. Show that every finite acyclic digraph has a sorted labeling.

If the vertices of a digraph with n vertices can have its vertices numbered from 1 to n such that i > j whenever there is a path from i to j, then such a labeling of its vertices is called sorted labeling. Show that every finite acyclic digraph has a sorted labeling.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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If the vertices of a digraph with n vertices can have its vertices numbered from 1 to n such that i > j whenever there is a path from i to j, then such a labeling of its vertices is called sorted labeling. Show that every finite acyclic digraph has a sorted labeling.
Transcribed Image Text:If the vertices of a digraph with n vertices can have its vertices numbered from 1 to n such that i > j whenever there is a path from i to j, then such a labeling of its vertices is called sorted labeling. Show that every finite acyclic digraph has a sorted labeling.
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