论文标题
关于最小素图的一代，结构和对称性
On the Generation, Structure, and Symmetries of Minimal Prime Graphs
论文作者
论文摘要
在本文中，我们继续研究有限解决基团的主要图。有限组G的Prime Graph或Gruenberg-Kegel图的顶点由G的序列组成，并且仅当G包含阶PQ元素时，从Primes P到Q的边缘。由于发现了2015年可解决方案组的素数简单，纯粹的图理论表征，因此从图理论角度进行了更详细的研究。在本文中，我们探讨了这些图形的几个新方面。我们表征了常规的发音图，并研究了任意基本图的效应图的自动形态。然后，我们通过用于基本图的新颖的常规图构造在较大的顶点集上研究最小的素数图，并通过在图形产品下证明质图属性的结果。最后，我们提出了与顶点重复不同的第一种新方法，以从给定的最小素图获得一个新的最小素图。
In this paper we continue the study of prime graphs of finite solvable groups. The prime graph, or Gruenberg-Kegel graph, of a finite group G has vertices consisting of the prime divisors of the order of G and an edge from primes p to q if and only if G contains an element of order pq. Since the discovery of a simple, purely graph theoretical characterization of the prime graphs of solvable groups in 2015 these graphs have been studied in more detail from a graph theoretic angle. In this paper we explore several new aspects of these graphs. We characterize regular reseminant graphs and study the automorphisms of reseminant graphs for arbitrary base graphs. We then study minimal prime graphs on larger vertex sets by a novel regular graph construction for base graphs and by proving results on prime graph properties under graph products. Lastly, we present the first new way, different from vertex duplication, to obtain a new minimal prime graph from a given minimal prime graph.
