A D18: Map $f : X \to Y$ is a

**graph isomorphism**with respect to $G_X$ and $G_Y$ if and only if

(1) | $f$ is a D4548: Graph homomorphism with respect to $G_X$ and $G_Y$ |

(2) | $f$ is an D976: Invertible map with an D216: Inverse map $f^{-1} : Y \to X$ |

(3) | $f^{-1}$ is a D4548: Graph homomorphism with respect to $G_Y$ and $G_X$ |