The number of maximal independent sets in a connected graph

• Published in: Discrete mathematics Vol. 68; no. 2; pp. 211 - 220
• Main Authors: Griggs, Jerrold R., Grinstead, Charles M., Guichard, David R.
• Format: Journal Article
• Language: English
• 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

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.