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.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter3: Matrices
Section3.7: Applications
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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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