@article{57ee310cd2a14779a9fe6f1f2f163e5a,
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.",
keywords = "Cayley graphs, Edge-regular graphs, Jacobi sums, Neumaier graphs, Regular cliques",
author = "{Abiad Monge}, Aida and Wouter Castryck and {De Boeck}, Maarten and Koolen, {Jack H.} and Sjanne Zeijlemaker",
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.",
year = "2023",
month = jan,
doi = "10.1016/j.jcta.2022.105684",
language = "English",
volume = "193",
journal = "Journal of Combinatorial Theory, Series A",
issn = "0097-3165",
publisher = "Academic Press Inc.",
}