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
Turán Graphs, Stability Number, and Fibonacci Index
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Maxima and Minima of the Hosoya Index and the Merrifield-Simmons Index
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
On the number of independent sets in cycle-separated tricyclic graphs
Computers & Mathematics with Applications
Graphs with given number of cut vertices and extremal Merrifield-Simmons index
Discrete Applied Mathematics
The number of independent sets of unicyclic graphs with given matching number
Discrete Applied Mathematics
Maximal independent sets in caterpillar graphs
Discrete Applied Mathematics
The smallest Merrifield-Simmons index of (n,n+1)-graphs
Mathematical and Computer Modelling: An International Journal
On the number of independent subsets in trees with restricted degrees
Mathematical and Computer Modelling: An International Journal
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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.