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 \(-2\).

中文翻译：

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特征值很少的Neumaier图

Neumaier图是包含规则集团的不完整的边缘正则图。在本文中，我们提供了一些充分必要的条件，以使Neumaier图成为强规则的。进一步地，我们表明不存在具有恰好四个不同特征值的Neumaier图。我们还确定特征值\（-2 \）最小的Neumaier图。