### Abstract

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.

Original language | English |
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Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 14 |

Volume | 2007-81 |

Publication status | Published - 2007 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2007-81 |

### Keywords

- Hamming graphs
- distance-regular graphs
- eigenvalues of graphs

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## Cite this

Bang, S., van Dam, E. R., & Koolen, J. H. (2007).

*Spectral Characterization of the Hamming Graphs*. (CentER Discussion Paper; Vol. 2007-81). Operations research.