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arXiv · 1406.4170

Godsil-McKay switching and isomorphism

Aida Abiad·Andries E. Brouwer·Willem H. Haemers
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Abstract

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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BibTeXRIS

Aida Abiad, Andries E. Brouwer, Willem H. Haemers. 2014-06-16. Godsil-McKay switching and isomorphism. https://arxiv.org/abs/1406.4170

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