# The number of maximal independent sets in a connected graph

@article{Griggs1988TheNO, title={The number of maximal independent sets in a connected graph}, author={J. R. Griggs and Charles M. Grinstead and D. Guichard}, journal={Discret. Math.}, year={1988}, volume={68}, pages={211-220} }

Abstract 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.

#### 77 Citations

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We find the maximum number of maximal independent sets in two families of graphs. The first family consists of all graphs with n vertices and at most r cycles. The second family is all graphs of the… Expand

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The maximum number of maximal independent sets among all bipartite graphs of order n and the extremal graphs as well as the corresponding results for connected bipartites graphs are determined. Expand

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