### Abstract

Original language | English |
---|---|

Pages (from-to) | 4-11 |

Journal | Electronic Journal of Linear Algebra |

Volume | 28 |

DOIs | |

Publication status | Published - 2015 |

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### Cite this

*Electronic Journal of Linear Algebra*,

*28*, 4-11. https://doi.org/10.13001/1081-3810.2986

}

*Electronic Journal of Linear Algebra*, vol. 28, pp. 4-11. https://doi.org/10.13001/1081-3810.2986

**Godsil-McKay switching and isomorphism,** / Abiad, Aida; Brouwer, A.E.; Haemers, W. H.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Godsil-McKay switching and isomorphism,

AU - Abiad, Aida

AU - Brouwer, A.E.

AU - Haemers, W. H.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

U2 - 10.13001/1081-3810.2986

DO - 10.13001/1081-3810.2986

M3 - Article

VL - 28

SP - 4

EP - 11

JO - Electronic Journal of Linear Algebra

JF - Electronic Journal of Linear Algebra

SN - 1081-3810

ER -