  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.
