Rhys Evans: Neumaier graphs

Abstract/Povzetek

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.