Cyclotomic matrices and graphs over the ring of integers of some imaginary quadratic fields

GD Taylor

doi:10.1016/j.jalgebra.2011.02.009

Cyclotomic matrices and graphs over the ring of integers of some imaginary quadratic fields

GD Taylor

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

9 Citations (Scopus)

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
Original language	English
Pages (from-to)	523 - 545
Number of pages	23
Journal	Journal of Algebra
Volume	331
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2011.02.009
Publication status	Published - Apr 2011

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Publisher: Elsevier

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10.1016/j.jalgebra.2011.02.009

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title = "Cyclotomic matrices and graphs over the ring of integers of some imaginary quadratic fields",

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.",

author = "GD Taylor",

note = "Publisher: Elsevier",

year = "2011",

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AB - 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.

U2 - 10.1016/j.jalgebra.2011.02.009

DO - 10.1016/j.jalgebra.2011.02.009

M3 - Article (Academic Journal)

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VL - 331

SP - 523

EP - 545

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

Cyclotomic matrices and graphs over the ring of integers of some imaginary quadratic fields

Abstract

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