Abstract
Denote bymi(G) the number of maximal independent sets ofG. This paper studies the setS(k) of all graphsG withmi(G) = k and without isolated vertices (exceptG ≅ K 1) or duplicated vertices. We determineS(1), S(2), andS(3) and prove that |V(G)| ≤ 2k−1 +k − 2 for anyG inS(k) andk ≥ 2; consequently,S(k) is finite for anyk.
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Supported in part by the National Science Council under grant NSC 83-0208-M009-050
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Jou, MJ., Chang, G.J., Lin, C. et al. A finiteness theorem for maximal independent sets. Graphs and Combinatorics 12, 321–326 (1996). https://doi.org/10.1007/BF01858464
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DOI: https://doi.org/10.1007/BF01858464