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

GD Taylor

Research output: Contribution to journalArticle (Academic Journal)peer-review

5 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 contributionCyclotomic matrices and graphs over the ring of integers of some imaginary quadratic fields
Original languageEnglish
Pages (from-to)523 - 545
Number of pages23
JournalJournal of Algebra
Volume331
Issue number1
DOIs
Publication statusPublished - Apr 2011

Bibliographical note

Publisher: Elsevier

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