Abstract The notion of a Riordan graph was introduced recently, and it is a far-reaching generalization of the well-known Pascal graphs and Toeplitz graphs. However, apart from a certain subclass of Toeplitz graphs, nothing was known on independent sets in Riordan graphs. In this paper, we give exact enumeration and lower and upper bounds for the number of independent sets for various classes of Riordan graphs. Remarkably, we offer a variety of methods to solve the problems that range from the structural decomposition theorem to methods in combinatorics on words. Some of our results are valid for any graph.

中文翻译：

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计算 Riordan 图中的独立集

摘要 Riordan 图的概念是最近引入的，它是著名的 Pascal 图和 Toeplitz 图的深远推广。然而，除了 Toeplitz 图的某个子类之外，Riordan 图的独立集上一无所知。在本文中，我们给出了各类 Riordan 图的独立集数的精确枚举和上下界。值得注意的是，我们提供了多种方法来解决从结构分解定理到单词组合学方法的问题。我们的一些结果适用于任何图形。