偶置乱图的张量幂幂的最大独立集和自同构群
Maximum-Size Independent Sets and Automorphism Groups of Tensor Powers of the Even Derangement Graphs
摘要：
令$A_n$是$X:=\{1,2,...,n\}$的偶排列的交替群，${\mathcal E}_n$是$X.$上的偶排列的集合。用$A\T_n^q$表示$A\T_n,$的$q$副本的张量积，其中凯莱图$A\T_n:=\T(A_n,{\mathcal E}_n)$被称为偶排列图。本文深入研究了$A\T_n^q$的连通性、直径、独立数、团数、色数以及$A\T_n^q.$的最大独立集等性质。利用关于最大独立集$A\T_n^q$的结果，完全确定了$A\T_n^q.$的全自同构群
英文摘要：
Let $A_n$ be the alternating group of even permutations of $X:=\{1,2,...,n\}$ and ${\mathcal E}_n$ the set of even derangements on $X.$ Denote by $A\T_n^q$ the tensor product of $q$ copies of $A\T_n,$ where the Cayley graph $A\T_n:=\T(A_n,{\mathcal E}_n)$ is called the even derangement graph. In this paper, we intensively investigate the properties of $A\T_n^q$ including connectedness, diameter, independence number, clique number, chromatic number and the maximum-size independent sets of $A\T_n^q.$ By using the result on the maximum-size independent sets $A\T_n^q$, we completely determine the full automorphism groups of $A\T_n^q.$
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
