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Do right-profiles determine graphs up to isomorphism?

For graphs $G$ and $H$, let $h(G,H)$ denote the number of graph homomorphisms from $G$ to $H$. Fix some enumeration $G_1,G_2,\ldots$ of (isomorphism classes of) the set $\mathbf{D}$ of finite graphs, ...
András Salamon's user avatar