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.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 80EQ
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc43bd3e6-5b65-4fb3-8d46-54613faca65d%2Fee7cb31b-c2ae-4c36-af11-ecd5a88fcdbd%2Fk7dfra_processed.png&w=3840&q=75)
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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