Neumaier graphs with few eigenvalues

Aida Abiad Monge; Bart De Bruyn; Jozefien D'haeseleer; Jack H. Koolen

doi:10.1007/s10623-021-00856-w

Neumaier graphs with few eigenvalues

Aida Abiad Monge (Corresponding author)
, Bart De Bruyn
, Jozefien D'haeseleer
, Jack H. Koolen

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

4 Citations (Scopus)

145 Downloads (Pure)

Abstract

A Neumaier graph is a non-complete edge-regular graph containing a regular clique. In this paper we give some sufficient and necessary conditions for a Neumaier graph to be strongly regular. Further we show that there does not exist Neumaier graphs with exactly four distinct eigenvalues. We also determine the Neumaier graphs with smallest eigenvalue - 2.

Original language	English
Pages (from-to)	2003-2019
Number of pages	17
Journal	Designs, Codes and Cryptography
Volume	90
Issue number	9
DOIs	https://doi.org/10.1007/s10623-021-00856-w
Publication status	Published - Sept 2022

Keywords

Edge-regular graph
Regular clique
Strongly regular graph

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10.1007/s10623-021-00856-w

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Cite this

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title = "Neumaier graphs with few eigenvalues",

abstract = "A Neumaier graph is a non-complete edge-regular graph containing a regular clique. In this paper we give some sufficient and necessary conditions for a Neumaier graph to be strongly regular. Further we show that there does not exist Neumaier graphs with exactly four distinct eigenvalues. We also determine the Neumaier graphs with smallest eigenvalue - 2.",

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AU - De Bruyn, Bart

AU - D'haeseleer, Jozefien

AU - Koolen, Jack H.

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AB - A Neumaier graph is a non-complete edge-regular graph containing a regular clique. In this paper we give some sufficient and necessary conditions for a Neumaier graph to be strongly regular. Further we show that there does not exist Neumaier graphs with exactly four distinct eigenvalues. We also determine the Neumaier graphs with smallest eigenvalue - 2.

KW - Edge-regular graph

KW - Regular clique

KW - Strongly regular graph

UR - https://www.scopus.com/pages/publications/85103659275

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DO - 10.1007/s10623-021-00856-w

M3 - Article

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JO - Designs, Codes and Cryptography

JF - Designs, Codes and Cryptography

IS - 9

ER -

Neumaier graphs with few eigenvalues

Abstract

Keywords

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