Lecture Content：

In the early 1980s, Neumaier explored regular cliques within edge-regular graphs, along with a specific class of designs characterized by their point graphs being strongly regular and containing regular cliques. This led to the question of the existence of a non-complete, edge-regular, non-strongly regular graph that includes a regular clique. Therefore, a strictly Neumaier graph is defined as a non-complete, edge-regular, non-strongly regular graph that encompasses a regular clique. The solution to this question was not discovered until 2018, and to date, only a few constructions for infinite families of strictly Neumaier graphs have been identified.

In this presentation, we will delve into the key findings concerning (strictly) Neumaier graphs, focusing particularly on their construction.

Speaker Introduction:

Dr. Rhys Evans is a postdoctoral researcher at the Institute of Mathematics, Physics, and Mechanics in Slovenia.