论文标题
可解决组的最小素图
Minimal Prime Graphs of Solvable Groups
论文作者
论文摘要
我们探索了有限溶剂组的最小素数图的图理论特性。在有限的群体理论中，研究一个小组的主要图是过去一个近半个世纪的重要话题。最近，仅以图形理论术语表征了可解决组的主要图。现在，这仅允许使用图理论的方法研究这些图。最小的素图被证明是特别感兴趣的，在本文中，我们通过探索直径，哈密顿周期以及对最小素数的自我平衡的特性，进一步探讨了这一点。我们还研究了一个新的但密切相关的素数概念，以最小化的素数，并研究最小的素数图。
We explore graph theoretical properties of minimal prime graphs of finite solvable groups. In finite group theory studying the prime graph of a group has been an important topic for the past almost half century. Recently prime graphs of solvable groups have been characterized in graph theoretical terms only. This now allows the study of these graphs with methods from graph theory only. Minimal prime graphs turn out to be of particular interest, and in this paper we pursue this further by exploring, among other things, diameters, Hamiltonian cycles and the property of being self-complementary for minimal prime graphs. We also study a new, but closely related notion of minimality for prime graphs and look into counting minimal prime graphs.
