Neumaier graphs with few eigenvalues

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

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
80 Downloads (Pure)


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 languageEnglish
Pages (from-to)2003-2019
Number of pages17
JournalDesigns, Codes and Cryptography
Issue number9
Publication statusPublished - Sept 2022


  • Edge-regular graph
  • Regular clique
  • Strongly regular graph


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