Grigorchuk群和Basilica群的Schreier图的Tutte多项式
The Tutte Polynomial of the Schreier graphs of the Grigorchuk group and the Basilica group
摘要：
研究了两个无限图族的Tutte多项式。这些是与两个著名的自相似群通过自同构作用于二元有根树的作用相关联的施赖尔图：第一个中间增长的格里戈丘克群，以及复多项式$z^2-1$的迭代单值群，称为Basilica群。对于这两个，我们描述的Tutte多项式，我们计算它的几个特殊的评价，这些图的组合结构提供进一步的信息。
英文摘要：
We study the Tutte polynomial of two infinite families of finite graphs. These are the Schreier graphs associated with the action of two well-known self-similar groups acting on the binary rooted tree by automorphisms: the first Grigorchuk group of intermediate growth, and the iterated monodromy group of the complex polynomial $z^2-1$ known as the Basilica group. For both of them, we describe the Tutte polynomial and we compute several special evaluations of it, giving further information about the combinatorial structure of these graphs.
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