论文标题
关于有限组的功率图的弦
On chordality of the power graph of finite groups
论文作者
论文摘要
如果该图禁止诱发长度为4或更多的串联，则称为弦。在本文中，我们试图识别其功率图是弦图的非努力组（Cameron在[4]中提出了这个问题）。在这个方向上，我们表征了具有和弦幂图的有限基团的直接乘积。我们对所有有限的谎言类型组有限组进行了分类，其功率图是和弦。此外，我们证明了零星简单组的功率图始终是非代码的。此外，我们表明，几乎所有最多47个订单组都具有弦式功率图。
A graph is called chordal if it forbids induced cycles of length 4 or more. In this paper, we attempt to identify the non-nilpotent groups whose power graph is a chordal graph (this question was raised by Cameron in [4]). In this direction, we characterise the direct product of finite groups having chordal power graphs. We classify all finite simple groups of Lie type whose power graph is chordal. Further, we prove that the power graph of a sporadic simple group is always non-chordal. In addition, we show that almost all groups of order up to 47 have chordal power graphs.
