  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.
