### Abstract

*H(3.q)*with diameter three is uniquely determined by its spectrum for q ≥ 36. Moreover, we show that for given integer D ≥ 2, any graph cospectral with the Hamming graph

*H(D,q)*is locally the disjoint union of

*D*copies of the complete graph of size

*q-1*, for q large enough.

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

Pages (from-to) | 2678-2686 |

Journal | Linear Algebra and its Applications |

Volume | 429 |

Issue number | 11-12 |

Publication status | Published - 2008 |

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### Cite this

*Linear Algebra and its Applications*,

*429*(11-12), 2678-2686.

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*Linear Algebra and its Applications*, vol. 429, no. 11-12, pp. 2678-2686.

**Spectral characterizations of the Hamming graph.** / Bang, S.; van Dam, E.R.; Koolen, J.H.

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

TY - JOUR

T1 - Spectral characterizations of the Hamming graph

AU - Bang, S.

AU - van Dam, E.R.

AU - Koolen, J.H.

N1 - Appeared earlier as CentER Discussion Paper 2007-81

PY - 2008

Y1 - 2008

N2 - We show that the Hamming graph H(3.q) with diameter three is uniquely determined by its spectrum for q ≥ 36. Moreover, we show that for given integer D ≥ 2, any graph cospectral with the Hamming graph H(D,q) is locally the disjoint union of D copies of the complete graph of size q-1, for q large enough.

AB - We show that the Hamming graph H(3.q) with diameter three is uniquely determined by its spectrum for q ≥ 36. Moreover, we show that for given integer D ≥ 2, any graph cospectral with the Hamming graph H(D,q) is locally the disjoint union of D copies of the complete graph of size q-1, for q large enough.

M3 - Article

VL - 429

SP - 2678

EP - 2686

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

IS - 11-12

ER -