论文标题
有限组的电源图
Power Graphs of Finite Groups
论文作者
论文摘要
组$ g $的电源图$ \ MATHCAL {p}（g）$是其顶点集为$ g $的图，如果一个是另一个角色，则在两个不同的顶点之间具有边缘。 $ g $的定向电源图$ \ vec {\ Mathcal {p}}（g）$是digraph，其顶点集为$ g $，在$ x $到$ y $中，$ x \ ne y $，$ x \ ne y $，每当$ y $都是$ y $的功率。我们从$ \ Mathcal {p}（g）$中重写了有关$ \ vec {\ Mathcal {p}}}（g）$的重建的两篇Cameron的文章。我们纠正了论文中出现的错误。特别是，我们添加了完成这些文章的主要定理所需的缺失案例。 我们还研究了一些等效关系下的功率图的商。我们以较低边界的最大循环图在组的功率图中关闭论文。
The power graph $\mathcal{P}(G)$ of a group $G$ is the graph whose vertex set is $G$, having an edge between two distinct vertices if one is the power of the other. The directed power graph $\vec{\mathcal{P}}(G)$ of a group $G$ is the digraph whose vertex set is $G$, having an arc from $x$ to $y$, with $x\ne y$, whenever $y$ is a power of $x$. We rewrite two Cameron's articles concerning the reconstruction of $\vec{\mathcal{P}}(G)$ from $\mathcal{P}(G)$. We correct mistakes that appear in the papers. In particular, we add missing cases needed to complete the main theorems of these articles. We also study the quotient of the power graph under some equivalence relations. We close the thesis with lower bounds for the maximum length of a cycle in the power graph of a group.
