The difference graph of a finite group is the difference of the enhanced power graph of and the power graph of , where all isolated vertices are removed. In this paper we study the connectedness and perfectness of with respect to various properties of the underlying group . We also find several connections between the difference graph of and the Gruenberg-Kegel graph of . We also examine the operation of twin reduction on graphs, a technique which produces smaller graphs which may be easier to analyze. Applying this technique to simple groups can have a number of outcomes, not fully understood, but including some graphs with large girth.

中文翻译：

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论增强幂图与有限群幂图的区别


有限群的差分图是 的增强幂图和 的幂​​图的差，其中所有孤立顶点都被移除。在本文中，我们研究了基础组的各种属性的连通性和完善性。我们还发现 的差异图和 的 Gruenberg-Kegel 图之间的一些联系。我们还研究了图上孪生约简的操作，这种技术可以生成更小的图，更容易分析。将这种技术应用于简单的组可能会产生许多结果，虽然尚未完全理解，但包括一些大周长的图表。