标题： 自相似图的概述，它们的推广及其相关的代数 显示英文标题

标题： An overview on self-similar graphs, their generalizations, and their associated algebras

摘要： 这些笔记最初是作为作者在CIMPA学校“K-理论与算子代数”上讲授的关于自相似图及其代数的入门课程的补充材料，该学校于2025年7月28日至8月8日在拉普拉塔和布宜诺斯艾利斯（阿根廷）举行。 在这些笔记中，我们介绍了与在图上作用的群相关的自相似图的概念。 我们使用不同的补充方法定义相应的$C^*$-代数，以理解其基本性质。 我们还分析了文献中出现的各种推广，并特别回顾了这种构造与Zappa-Szép乘积之间的关系。 最后，我们介绍了这些代数在同调和$K$-理论方面的最新成果。 显示英文摘要

摘要： These notes were originally intended to be complementary material for an introductory course on self-similar graphs and their algebras, presented by the author at the CIMPA School ``K-theory and Operator Algebras'', held in La Plata and Buenos Aires (Argentina) from 28 July to 8 August 2025. In these notes, we introduce the concept of self-similar graph, associated with groups acting on graphs. We define the corresponding $C^*$-algebra using different complementary approaches, to understand its basic properties. We also analyze various generalizations that appear in the literature and, in particular, review the relationship of this construction with Zappa-Sz\'ep products. Finally, we present very recent results on homology and $K$-theory for these algebras.