Integral Cayley multigraphs over abelian and Hamiltonian groups
type: Item
instance of: scholarly article
title: Integral Cayley multigraphs over abelian and Hamiltonian groups
zbMATH Open document ID: 1298.05158
author: Matt DeVos
author: Roi Krakovski
author: Bojan Mohar
author: Azhvan Sheikh Ahmady
published in: The Electronic Journal of Combinatorics
publication date: 2014-08-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1209.5126
full work available at URL: v20i2p63
review text: Summary: It is shown that a Cayley multigraph over a group \(G\) with generating multiset \(S\) is integral (i.e., all of its eigenvalues are integers) if \(S\) lies in the integral cone over the boolean algebra generated by the normal subgroups of \(G\). The converse holds in the case when \(G\) is abelian. This in particular gives an alternative, character theoretic proof of a theorem of \textit{W. G. Bridges} and \textit{R. A. Mena} [J. Comb. Theory, Ser. A 32, 264--280 (1982; Zbl 0485.05040)]. We extend this result to provide a necessary and sufficient condition for a Cayley multigraph over a Hamiltonian group to be integral, in terms of character sums and the structure of the generating set.
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05E15
zbMATH DE Number: 6330271
zbMATH Keywords: Cayley graph
zbMATH Keywords: integral eigenvalue
zbMATH Keywords: abelian group
zbMATH Keywords: Hamiltonian group
MaRDI profile type: Publication
arXiv ID: 1209.5126
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description: scientific article; zbMATH DE number 6330271