Lighter群，de Bruijn图，蛛网图及其谱
Lamplighter groups, de Bruijn graphs, spider-web graphs and their spectra
摘要：
我们描述了蜘蛛网图$S_{k,M,N }$，$k \geq 2$，$M \geq 1$和$N \geq 0$的无限族，在物理文献中作为著名的de Brujin图$B_{k,N}$和循环图$C_M$的张量积进行研究，并证明了这些图是点灯群$L_k = Z/kZ \wr Z$的Schreier图。这使我们能够计算它们的光谱，并确定$S_{k,M,N}$的无限极限，作为$N, M \to\infty$，与点灯人组$L_k$的凯莱图。这是文章的最终版本，考虑了参考者的评论和扩展的介绍。
英文摘要：
We describe the infinite family of spider-web graphs $S_{k,M,N }$, $k \geq 2$, $M \geq 1$ and $N \geq 0$, studied in physical literature as tensor products of well-known de Brujin graphs $B_{k,N}$ and cyclic graphs $C_M$ and show that these graphs are Schreier graphs of the lamplighter groups $L_k = Z/kZ \wr Z$. This allows us to compute their spectra and to identify the infinite limit of $S_{k,M,N}$, as $N, M \to\infty$, with the Cayley graph of the lamplighter group $L_k$. This is the final version of the article, taking in account comments from the referees and with an extended introduction.
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。
