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Problem 4. Define the notion of isomorphism and vertex-transitivity for digraphs. Then prove that every vertex-transitive digraph is diregular. Problem 5. Show that every nontrivial acyclic graph has at least two vertices of degree less than two.

Problem 4. Define the notion of isomorphism and vertex-transitivity for digraphs. Then prove that every vertex-transitive digraph is diregular. Problem 5. Show that every nontrivial acyclic graph has at least two vertices of degree less than two.

Linear Algebra: A Modern Introduction
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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Problem 4. Define the notion of isomorphism and vertex-transitivity for digraphs. Then prove that every vertex-transitive digraph is diregular. Problem 5. Show that every nontrivial acyclic graph has at least two vertices of degree less than two.
Transcribed Image Text:Problem 4. Define the notion of isomorphism and vertex-transitivity for digraphs. Then prove that every vertex-transitive digraph is diregular. Problem 5. Show that every nontrivial acyclic graph has at least two vertices of degree less than two.
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