Definition:Homomorphism (Graph Theory)

Definition
Let $G = \struct {\map V G, \map E G}$ and $H = \struct {\map V H, \map E H}$ be graphs.

Let there exist a mapping $F: \map V G \to \map V H$ such that:
 * for each edge $\set {u, v} \in \map E G$
 * there exists an edge $\set {\map F u, \map F v} \in \map E H$.

Then $G$ and $H$ are homomorphic.

The mapping $F$ is called a homomorphism from $G$ to $H$.