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Non-isomorphic graphs with identical iterated degree matrix

Yes. Consider all graphs with $V=\{1,\ldots,n\}$ for which the vertex $n$ has degree $n-1$. There are $2^{n^2/2+o(n^2)}$ isomorphism classes of such graphs. But $\deg_k(v)=n$ for all $v$ and all $k\...
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