The number of maximal independent sets in a tree
SIAM Journal on Algebraic and Discrete Methods
Graphs & digraphs (2nd ed.)
The number of maximal independent sets in a connected graph
Discrete Mathematics
On generating all maximal independent sets
Information Processing Letters
A note on independent sets in trees
SIAM Journal on Discrete Mathematics
Bipartite graphs can have any number of independent sets
Discrete Mathematics
The structure and maximum number of maximum independent sets in trees
Journal of Graph Theory
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A maximal independent set of a graph G is an independent set that is not contained properly in any other independent set of G. Let i(G) denote the number of maximal independent sets of G. Here, we prove two conjectures, suggested by P. Erdös, that the maximum number of maximal independent sets among all graphs of order n in a family Φ is o(3n/3) if Φ is either a family of connected graphs such that the largest value of maximum degrees among all graphs of order n in Φ is o(n) or a family of graphs such that the approaches infinity as n → ∞. © 1994 Wiley Periodicals, Inc.