A general construction of strictly Neumaier graphs and a related switching

We present a construction of Neumaier graphs with nexus 1, which generalises two known constructions of Neumaier graphs. We also use W. Wang, L. Qiu, and Y. Hu switching to show that we construct cospectral Neumaier graphs. Finally, we show that several small strictly Neumaier graphs can be obtained from our construction, and give a geometric or algebraic description for each of these graphs.