Graph Homomorphism

• A homomorphism between graphs and is a mapping such that

  • For digraphs, homomorphisms preserve direction. That is

• (Godsil e1.4) If is a homomorphism from to and . Then

• An endomorphism is a homomorphism of the form .

  The set of all endomorphisms of is the endomorphism monoid .

Retracts §

• A homomorphism is a retraction from to , where if

  If a retraction exists, we say is a retract of .

Topics §

• Graph Isomorphism
• Graph Automorphism

Links §

• Introduction To Graph Theory by Wilson

• Algebraic Graph Theory by Godsil and Royle

• Fundamental Constructs of Group Theory

• Families of Graphs