ThmDex – An index of mathematical definitions, results, and conjectures.
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Zermelo-Fraenkel set theory
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Definition D4550
Graph intersection
Formulation 0
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 an intersection of $G_X$ and $G_Y$ if and only if
(1) $Z = X \cap Y$ (D76: Set intersection)
(2) $\mathcal{E}_Z = \mathcal{E}_X \cap \mathcal{E}_Y$ (D76: Set intersection)