论文标题
有限简单组的功率图的lambda数
The Lambda Number of the Power Graph of Finite Simple Groups
论文作者
论文摘要
对于有限的组$ g $，功率图$γ_g$是一个图表，其顶点等于$ g $，而当其中一个是另一个是另一个的正整数量时，$ g $的两个截然不同的元素才相邻。 $ l（2,1）$ - $γ_g$的标记是在$ g $上定义的整数值函数，因此两个相邻顶点的图像（分别为距离两个）的图像之间的距离至少为两个（至少两个）。 lambda数字$λ（g）$被定义为最大和最小的整数值之间的最小差异，分配给所有可能的$ l（2,1）$ - 标记为$γ_g$的顶点。众所周知，$λ（g）\ geq | g | $。在本文中，我们证明，如果$ g $是一个有限的简单组，则$λ（g）= | g | $，除非$ g $是Prime Order的循环时。这解决了有限组$ g $的部分分类，该$ g $实现了lambda编号的下限。
For a finite group $G$, the power graph $Γ_G$ is a graph whose set of vertices is equal to $G$ and two distinct elements of $G$ are adjacent if and only if one of them is a positive integer power of the other. An $L(2,1)$-labelling of $Γ_G$ is an integer-valued function defined on $G$ so that the distance between the images of two adjacent vertices (resp. vertices with distance two) are at least two (resp. at least one). The lambda number $λ(G)$ is defined to be the least difference between the largest and the smallest integer values assigned to the vertices of $Γ_G$ for all possible $L(2,1)$-labellings of $Γ_G$. It is known that $λ(G) \geq |G|$. In this paper, we prove that if $G$ is a finite simple group, then $λ(G) = |G|$ except when $G$ is cyclic of prime order. This settles a partial classification of finite groups $G$ that achieve the lower bound on of lambda number.
