The number of maximal independent sets in a connected graph

We determine the maximum number of maximal independent sets which a connected graph on n vertices can have, and we completely characterize the extremal graphs, thereby answering a question of Wilf.

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Bibliographic Details
Published inDiscrete mathematics Vol. 68; no. 2; pp. 211 - 220
Main Authors Griggs, Jerrold R., Grinstead, Charles M., Guichard, David R.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 1988
Elsevier
Subjects
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Mathematics
Sciences and techniques of general use
Connected graph
Graph theory
Clique graph
Extremum problem
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Summary:We determine the maximum number of maximal independent sets which a connected graph on n vertices can have, and we completely characterize the extremal graphs, thereby answering a question of Wilf.
ISSN:0012-365X
1872-681X
DOI:10.1016/0012-365X(88)90114-8