A note on eigenvalues of Cayley graphs

Arnbjörg Soffía Árnadóttir; Chris Godsil

doi:10.1016/j.laa.2023.12.002

A note on eigenvalues of Cayley graphs

Arnbjörg Soffía Árnadóttir^*
, Chris Godsil

^*Corresponding author for this work

University of Waterloo

Research output: Contribution to journal › Journal article › Research › peer-review

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Abstract

A graph is called integral if all its eigenvalues are integers. A Cayley graph is called normal if its connection set is a union of conjugacy classes. We show that a non-empty integral normal Cayley graph for a group of odd order has an odd eigenvalue.

Original language	English
Journal	Linear Algebra and Its Applications
Volume	721
Pages (from-to)	240-249
ISSN	0024-3795
DOIs	https://doi.org/10.1016/j.laa.2023.12.002
Publication status	Published - 2025

Keywords

Association schemes
Cayley graphs
Eigenvalues

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10.1016/j.laa.2023.12.002

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title = "A note on eigenvalues of Cayley graphs",

abstract = "A graph is called integral if all its eigenvalues are integers. A Cayley graph is called normal if its connection set is a union of conjugacy classes. We show that a non-empty integral normal Cayley graph for a group of odd order has an odd eigenvalue.",

keywords = "Association schemes, Cayley graphs, Eigenvalues",

author = "{\'A}rnad{\'o}ttir, \{Arnbj{\"o}rg Soff{\'i}a\} and Chris Godsil",

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year = "2025",

doi = "10.1016/j.laa.2023.12.002",

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T1 - A note on eigenvalues of Cayley graphs

AU - Árnadóttir, Arnbjörg Soffía

AU - Godsil, Chris

PY - 2025

Y1 - 2025

N2 - A graph is called integral if all its eigenvalues are integers. A Cayley graph is called normal if its connection set is a union of conjugacy classes. We show that a non-empty integral normal Cayley graph for a group of odd order has an odd eigenvalue.

AB - A graph is called integral if all its eigenvalues are integers. A Cayley graph is called normal if its connection set is a union of conjugacy classes. We show that a non-empty integral normal Cayley graph for a group of odd order has an odd eigenvalue.

KW - Association schemes

KW - Cayley graphs

KW - Eigenvalues

U2 - 10.1016/j.laa.2023.12.002

DO - 10.1016/j.laa.2023.12.002

M3 - Journal article

AN - SCOPUS:85181084053

SN - 0024-3795

VL - 721

SP - 240

EP - 249

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

A note on eigenvalues of Cayley graphs

Abstract

Keywords

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