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arXiv · 2012.08390

Switching for Small Strongly Regular Graphs

Ferdinand Ihringer
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Abstract

We provide an abundance of strongly regular graphs (SRGs) for certain parameters $(n, k, \lambda, \mu)$ 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 Kr\v{c}adinac partial geometry, thus finding a third method of constructing it.

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Ferdinand Ihringer. 2020-12-15. Switching for Small Strongly Regular Graphs. https://arxiv.org/abs/2012.08390

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