Paper detail

Switching for Small Strongly Regular Graphs

We provide an abundance of strongly regular graphs (SRGs) for certain parameters $(n, k, λ, μ)$ with $n < 100$. For this we use Godsil-McKay (GM) switching with a partition of type $4,n-4$ and Wang-Qiu-Hu (WQH) switching with a partition of type $3,3,n-6$ or $4,4,n-8$. In most cases, we start with a highly symmetric graph which belongs to a finite geometry. Many of the obtained graphs are new; for instance, we find 16565438 strongly regular graphs with parameters $(81, 30, 9, 12)$ while only 15 seem to be described in the literature. We provide statistics about the size of the occurring automorphism groups. We also find the recently discovered Krčadinac partial geometry, thus finding a third method of constructing it.