The number of independent sets in unicyclic graphs

Authors:
Anders Sune Pedersen;Preben Dahl Vestergaard
Affiliations:
Department of Mathematics, Aalborg University, Aalborg Øst, Denmark;Department of Mathematics, Aalborg University, Aalborg Øst, Denmark
Venue:
Discrete Applied Mathematics
Year:
2005

Citing 2
Cited 4

On the hardness of approximate reasoning

Artificial Intelligence
Maximal independent sets in graphs with at most one cycle

Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization

Note: Fibonacci numbers and Lucas numbers in graphs

Discrete Applied Mathematics
The number of independent sets in unicyclic graphs with a given diameter

Discrete Applied Mathematics
On the extremal Merrifield-Simmons index and Hosoya index of quasi-tree graphs

Discrete Applied Mathematics
Tricyclic graphs with maximum Merrifield-Simmons index

Discrete Applied Mathematics

Quantified Score

Hi-index	0.04

Visualization

Abstract

In this paper, we determine upper and lower bounds for the number of independent sets in a unicyclic graph in terms of its order. This gives an upper bound for the number of independent sets in a connected graph which contains at least one cycle. We also determine the upper bound for the number of independent sets in a unicyclic graph in terms of order and girth. In each case, we characterize the extremal graphs.