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Homomorphic equivalence

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In graph theory, a branch of mathematics, two graphs G and H are called homomorphically equivalent if there exists a graph homomorphism f : G → H {\displaystyle f\colon G\to H} and a graph homomorphism g : H → G {\displaystyle g\colon H\to G} . An example usage of this notion is that any two cores of a graph are homomorphically equivalent.