Week 2 Morphisms of graphs

Question 1

Morphism

Answer 1

Let G= (V,E,ε) and G′= (V′,E′,ε′) be graphs. A
morphism (or map) of graphs is a pair of functions
ϕ: V →V′and ψ: E →E′satisfying
ε′◦ψ= ϕ∗◦ε.

Question 2

Special morphisms (embedding)

Answer 2

G is a subgraph of H iff there is a morphism
(ϕ,ψ) : G→H with ϕ and ψ both injective. We say
that (ϕ,ψ) is an embedding.

Question 3

Special morphisms (cover)

Answer 3

If ϕ and ψ are both surjective, then we call the
morphism (ϕ,ψ) a cover.