Distinguishing graphs by the number of homomorphisms
A homomorphism from one graph to another is a mapping that sends vertices to vertices and edges to edges. Let \(|G\to H|\) denote the number of homomorphisms from \(G\) to \(H\). For example \(|G\to K_n|\) is the number of \(n\)-colorings of \(G\). If \(\mathcal F\) is a collection of graphs, we say that \(\mathcal F\) distinguishes graphs \(G\) and ...
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