Geodesic
Distinguishing graphs by the number of homomorphisms
Discussiones Mathematicae. Graph Theory, Tome 15 (1995) no. 1, pp. 73-75.

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A homomorphism from one graph to another is a map that sends vertices to vertices and edges to edges. We denote the number of homomorphisms from G to H by |G → H|. If is a collection of graphs, we say that distinguishes graphs G and H if there is some member X of such that |G → X | ≠ |H → X|. is a distinguishing family if it distinguishes all pairs of graphs.
Keywords: graph homomorphism, chromatic number 
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Fisk, Steve. Distinguishing graphs by the number of homomorphisms. Discussiones Mathematicae. Graph Theory, Tome 15 (1995) no. 1, pp. 73-75. http://geodesic.mathdoc.fr/item/DMGT_1995_15_1_a7/

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