On graphs with the third largest number of maximal independent sets

Authors:
Hongbo Hua;Yaoping Hou
Affiliations:
Department of Computing Science, Huaiyin Institute of Technology, Huaian, Jiangsu 223000, PR China;College of Mathematics and Computer, Hunan Normal University, Changsha, Hunan 410081, PR China
Venue:
Information Processing Letters
Year:
2009

Citing 9
Cited 0

The number of maximal independent sets in a tree

SIAM Journal on Algebraic and Discrete Methods
The number of maximal independent sets in a connected graph

Discrete Mathematics
A note on independent sets in trees

SIAM Journal on Discrete Mathematics
The number of maximal independent sets in triangle-free graphs

SIAM Journal on Discrete Mathematics
Maximal independent sets in graphs with at most one cycle

Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
The number of maximal independent sets in connected triangle-free graphs

Discrete Mathematics
Graph Theory With Applications

Graph Theory With Applications
Maximal independent sets in graphs with at most r cycles

Journal of Graph Theory
Maximal and maximum independent sets in graphs with at most r cycles

Journal of Graph Theory

Quantified Score

Hi-index	0.89

Visualization

Abstract

Let G be a simple and undirected graph. By mi(G) we denote the number of maximal independent sets in G. Erdos and Moser posed the problem to determine the maximum cardinality of mi(G) among all graphs of order n and to characterize the corresponding extremal graphs attaining this maximum cardinality. The above problem has been solved by Moon and Moser in [J.W. Moon, L. Moser, On cliques in graphs, Israel J. Math. 3 (1965) 23-28]. More recently, Jin and Li [Z. Jin, X. Li, Graphs with the second largest number of maximal independent sets, Discrete Mathematics 308 (2008) 5864-5870] investigated the second largest cardinality of mi(G) among all graphs of order n and characterized the extremal graph attaining this value of mi(G). In this paper, we shall determine the third largest cardinality of mi(G) among all graphs G of order n. Additionally, graphs achieving this value are also determined.