Godsil-McKay switching and isomorphism,
Abiad,Aida Brouwer,A.E. Haemers,W. H.
Abiad,Aida
Brouwer,A.E.
Haemers,W. H.
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 sucient condition for being isomorphic after switching, and give examples which show that this condition is not necessary. For some graph products we obtain sucient conditions for being non-isomorphic after switching. As an example we nd that the tensor product of the grid L(';m) (' > m 2) and a graph with at least one vertex of degree two is not determined by its adjacency spectrum.
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Date
2015
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Research Projects
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Abiad, A, Brouwer, A E & Haemers, W H 2015, 'Godsil-McKay switching and isomorphism,', Electronic Journal of Linear Algebra, vol. 28, pp. 4-11. https://doi.org/10.13001/1081-3810.2986