论文标题
有限组的电源图
Power Graphs of Finite Group
论文作者
论文摘要
组的定向功率图是一个图形，其顶点集是该组的元素，如果$ y $是$ x $的电源，则其边缘从$ x $ $ y $。可以通过迷失其边缘来从定向的电源图获得组的\ textit {power graph}。本文讨论了有限组的功率图中集团，周期，路径和着色的特性。给出了循环基团的功率图中最长的定向路径的结构，以及功率图中的距离的一些结果。我们讨论了一个组的环状亚组图，并表明它与功率图共享大量的属性，包括独立数，完整性，孔数等，但少数例外，例如平面和哈密顿式。
The Directed Power Graph of a group is a graph whose vertex set is the elements of the group, with an edge from $x$ to $y$ if $y$ is a power of $x$. The \textit{Power Graph} of a group can be obtained from the directed power graph by disorienting its edges. This article discusses properties of cliques, cycles, paths, and coloring in power graphs of finite groups. A construction of the longest directed path in power graphs of cyclic groups is given, along with some results on distance in power graphs. We discuss the cyclic subgroup graph of a group and show that it shares a remarkable number of properties with the power graph, including independence number, completeness, number of holes etc., with a few exceptions like planarity and Hamiltonian.
