论文标题
切换小规则的图形
Switching for Small Strongly Regular Graphs
论文作者
论文摘要
我们为某些参数$（n，k，λ，μ）$提供了丰富的常规图（SRG），$ n <100 $。为此，我们使用Godsil-McKay（GM）切换，分区$ 4，N-4 $和Wang-QIU-HU（WQH）切换，分区的分区$ 3,3,3，N-6 $或$ 4,4,4，N-8 $。在大多数情况下，我们从属于有限几何形状的高度对称图开始。许多获得的图是新的。例如，我们发现16565438具有参数$（81、30、9、12）$的强烈规则图，而文献中似乎只有15个。 我们提供有关发生的自多态群体规模的统计数据。我们还发现了最近发现的Krčadinac部分几何形状，因此找到了构造它的第三种方法。
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.
