## Abstract

We determine all Hermitian -matrices for which every eigenvalue is in the interval [−2,2], for each d∈{−2,−7,−11,−15}. To do so, we generalise charged signed graphs to L-graphs for appropriate finite sets L, and classify all L-graphs satisfying the same eigenvalue constraints. We find that, as in the integer case, any such matrix/graph is contained in a maximal example with all eigenvalues ±2.

Translated title of the contribution | Cyclotomic matrices and graphs over the ring of integers of some imaginary quadratic fields |
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Original language | English |

Pages (from-to) | 523 - 545 |

Number of pages | 23 |

Journal | Journal of Algebra |

Volume | 331 |

Issue number | 1 |

DOIs | |

Publication status | Published - Apr 2011 |