Graph homomorphism

Let $G_X = (X, \mathcal{E}_X)$ and $G_Y = (Y, \mathcal{E}_Y)$ each be a D778: Graph.
A D18: Map $f : X \to Y$ is a graph homomorphism with respect to $G_X$ and $G_Y$ if and only if $$\forall \, x, y \in X \, (\{ x, y \} \in \mathcal{E}_X \quad \Rightarrow \quad \{ f(x), f(y) \} \in \mathcal{E}_Y)$$
Child definitions