讲座内容：

In the early 1980s, Neumaier studied regular cliques in edge-regular graphs, and a certain class of designs whose point graphs are strongly regular and contain regular cliques. He then posed the problem of whether there exists a non-complete, edge-regular, non-strongly regular graph containing a regular clique. We thus define a strictly Neumaier graph to be a non-complete, edge-regular, non-strongly regular graph containing a regular clique. It was not until 2018 that a solution to this problem was given, and currently only a handful of constructions for infinite families of strictly Neumaier graphs are known.

In this talk we will review the major results regarding (strictly) Neumaier graphs, with an emphasis on the construction of Neumaier graphs.