Let G be a DAG with exactly one source r and such that for any vertex v there exists a unique directed path from r to v. Let G" be the graph obtained by erasing the direction on each edge of G. Prove that (G",r) is a rooted tree.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
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3.
Let G be a DAG with exactly one source r and such that for any vertex v there exists a unique
directed path from r to v. Let G" be the graph obtained by erasing the direction on each edge
of G. Prove that (G", r) is a rooted tree.
Transcribed Image Text:3. Let G be a DAG with exactly one source r and such that for any vertex v there exists a unique directed path from r to v. Let G" be the graph obtained by erasing the direction on each edge of G. Prove that (G", r) is a rooted tree.
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