Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Godsil-McKay switching and isomorphism   Godsil-McKay switching is an operation on graphs that doesn't change the
spectrum of the adjacency matrix. Usually (but not always) the obtained graph
is non-isomorphic with the original graph. We present a straightforward
sufficient condition for being isomorphic after switching, and give examples
which show that this condition is not necessary. For some graph products we
obtain sufficient conditions for being non-isomorphic after switching. As an
example we find that the tensor product of the $\ell\times m$ grid ($\ell>m\geq
2$) and a graph with at least one vertex of degree two is not determined by its
adjacency spectrum.

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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
1
The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: physics