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Definition D4509
Graph tensor product

Let $G_X = (X, \mathcal{E}_X)$ and $G_Y = (Y, \mathcal{E}_Y)$ each be a D778: Graph.
An D548: Ordered pair $G_Z = (Z, \mathcal{E}_Z)$ is a tensor product of $G_X$ and $G_Y$ if and only if
 (1) $Z = X \times Y$ (D326: Cartesian product) (2) $\mathcal{E}_Z = \{ x y = (x_1, x_2)(y_1, y_2) : x_1 y_1 \in \mathcal{E}_X \text{ and } x_2 y_2 \in \mathcal{E}_Y \}$

Let $G_X = (X, \mathcal{E}_X)$ and $G_Y = (Y, \mathcal{E}_Y)$ each be a D778: Graph.
An D548: Ordered pair $G_Z = (Z, \mathcal{E}_Z)$ is a tensor product of $G_X$ and $G_Y$ if and only if
 (1) $Z = X \times Y$ (D326: Cartesian product) (2) $\mathcal{E}_Z = \{ \{ (x_1, x_2), (y_1, y_2) \} : \{ x_1, y_1 \} \in \mathcal{E}_X \text{ and } \{ x_2, y_2 \} \in \mathcal{E}_Y \}$