Maximal Independent Sets in Polygonal Cacti
Combinatorics
2022-05-23 v2
Abstract
Counting the number of maximal independent sets of graphs was started over years ago by Erd\H{o}s and Mooser. The problem has been continuously studied with a number of variations. Interestingly, when the maximal condition of an independent set is removed, such the concept presents one of topological indices in molecular graphs, the so called Merrifield-Simmons index. In this paper, we applied the concept of bivariate generating function to establish the recurrence relations of the numbers of maximal independent sets of regualr -gonal cacti when . By the ideas on meromorphic functions and the growth of power series coefficients, the asymptotic behaviors through simple functions of these recurrence relations have been established.
Cite
@article{arxiv.2202.11294,
title = {Maximal Independent Sets in Polygonal Cacti},
author = {Natawat Klamsakul and Pantaree Thengarnanchai and Mattanaporn Suebtangjai and Pailin Kaewperm and Nuttanon Songsuwan and Pawaton Kaemawichanurat},
journal= {arXiv preprint arXiv:2202.11294},
year = {2022}
}