The Number of Maximal Independent Sets in Quasi-Tree Graphs and Quasi-Forest Graphs

Jenq-Jong Lin, Min-Jen Jou
2017 Open Journal of Discrete Mathematics  
A maximal independent set is an independent set that is not a proper subset of any other independent set. A connected graph (respectively, graph) G with vertex set ( ) In this paper, we survey on the large numbers of maximal independent sets among all trees, forests, quasi-trees and quasi-forests. In addition, we further look into the problem of determining the third largest number of maximal independent sets among all quasi-trees and quasi-forests. Extremal graphs achieving these values are
more » ... o given. Keywords Maximal Independent Set, Quasi-Tree Graph, Quasi-Forest Graph, Extremal Graph ( ) mi G among all graphs of order n; Jou and Lin [4] further explored the same problem for trees and forests; Jin and Yan [5] solved the third largest number of How to cite this paper: Lin,
doi:10.4236/ojdm.2017.73013 fatcat:vq5uhahilrarxdjtf2bqw2vdza