Counting independent sets in Riordan graphs
Combinatorics
2020-07-01 v1
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.
Keywords
Cite
@article{arxiv.2006.16579,
title = {Counting independent sets in Riordan graphs},
author = {Gi-Sang Cheon and Ji-Hwan Jung and Bumtle Kang and Hana Kim and Suh-Ryung Kim and Sergey Kitaev and Seyed Ahmad Mojallal},
journal= {arXiv preprint arXiv:2006.16579},
year = {2020}
}
Comments
Accepted for publication in Discrete Mathematics