Strongly cospectral vertices in normal Cayley graphs

We prove an upper bound on the number of pairwise strongly cospectral vertices in a normal Cayley graph, in terms of the multiplicities of its eigenvalues. We use this to determine an explicit bound in Cayley graphs of \(\mathbb{Z}_2^d\) and \(\mathbb{Z}_4^d\). We also provide some infinite families...

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Bibliographic Details
Published in:arXiv.org 2023-01
Main Authors: Arnbjörg Soffía Árnadóttir, Godsil, Chris
Format: Article
Language:English
Subjects:
Apexes
Eigenvalues
Graph theory
Graphs
Upper bounds
Online Access:Get full text
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Summary:We prove an upper bound on the number of pairwise strongly cospectral vertices in a normal Cayley graph, in terms of the multiplicities of its eigenvalues. We use this to determine an explicit bound in Cayley graphs of \(\mathbb{Z}_2^d\) and \(\mathbb{Z}_4^d\). We also provide some infinite families of Cayley graphs of \(\mathbb{Z}_2^d\) with a set of four pairwise strongly cospectral vertices and show that such graphs exist in every dimension.
ISSN:2331-8422
DOI:10.48550/arxiv.2109.07568