An infinite class of Neumaier graphs and non-existence results

Aida Abiad Monge; Wouter Castryck; Maarten De Boeck; Jack H. Koolen; Sjanne Zeijlemaker

doi:10.1016/j.jcta.2022.105684

An infinite class of Neumaier graphs and non-existence results

Aida Abiad Monge, Wouter Castryck, Maarten De Boeck (Corresponding author), Jack H. Koolen, Sjanne Zeijlemaker

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

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Abstract

A Neumaier graph is a non-complete edge-regular graph containing a regular clique. A Neumaier graph that is not strongly regular is called a strictly Neumaier graph. In this work we present a new construction of strictly Neumaier graphs, and using Jacobi sums, we show that our construction produces infinitely many instances. Moreover, we prove some necessary conditions for the existence of (strictly) Neumaier graphs that allow us to show that several parameter sets are not admissible.

Original language	English
Article number	105684
Number of pages	30
Journal	Journal of Combinatorial Theory, Series A
Volume	193
DOIs	https://doi.org/10.1016/j.jcta.2022.105684
Publication status	Published - Jan 2023

Bibliographical note

Funding Information:
Aida Abiad is partially supported by the FWO (Research Foundation Flanders, No 1285921N ). Wouter Castryck is supported by the Research Council, KU Leuven grant C14/18/067 and by CyberSecurity Research Flanders with reference VR20192203 . Jack H. Koolen is partially supported by the National Natural Science Foundation of China (No. 12071454 ), Anhui Initiative in Quantum Information Technologies (No. AHY150000 ) and the National Key R&D Program of China (No. 2020YFA0713100 ).

Publisher Copyright:
© 2022 Elsevier Inc.

Keywords

Cayley graphs
Edge-regular graphs
Jacobi sums
Neumaier graphs
Regular cliques

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title = "An infinite class of Neumaier graphs and non-existence results",

abstract = "A Neumaier graph is a non-complete edge-regular graph containing a regular clique. A Neumaier graph that is not strongly regular is called a strictly Neumaier graph. In this work we present a new construction of strictly Neumaier graphs, and using Jacobi sums, we show that our construction produces infinitely many instances. Moreover, we prove some necessary conditions for the existence of (strictly) Neumaier graphs that allow us to show that several parameter sets are not admissible.",

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note = "Funding Information: Aida Abiad is partially supported by the FWO (Research Foundation Flanders, No 1285921N ). Wouter Castryck is supported by the Research Council, KU Leuven grant C14/18/067 and by CyberSecurity Research Flanders with reference VR20192203 . Jack H. Koolen is partially supported by the National Natural Science Foundation of China (No. 12071454 ), Anhui Initiative in Quantum Information Technologies (No. AHY150000 ) and the National Key R&D Program of China (No. 2020YFA0713100 ). Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

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AU - Zeijlemaker, Sjanne

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KW - Jacobi sums

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An infinite class of Neumaier graphs and non-existence results

Abstract

Bibliographical note

Keywords

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