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
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
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by using python do the following problems 

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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