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The Number of Maximal Independent Sets in a Tree

✍ Scribed by Wilf, Herbert S.

Book ID
118213024
Publisher
Society for Industrial and Applied Mathematics
Year
1986
Weight
451 KB
Volume
7
Category
Article
ISSN
0196-5212

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πŸ“œ SIMILAR VOLUMES

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✍ Jerrold R. Griggs; Charles M. Grinstead; David R. Guichard πŸ“‚ Article πŸ“… 1988 πŸ› Elsevier Science 🌐 English βš– 1021 KB

We determine the maximum on n vertices can have, and we a question of Wilf. number of maximal independent sets which a connected graph completely characterize the extremal graphs, thereby answering \* Partially supported by NSF grant number DIMS-8401281. t Partially supported by NSF grant number D S

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Generalizing a theorem of Moon and Moser. we determine the maximum number of maximal independent sets in a connected graph on n vertices for n sufficiently large, e.g., n > 50. = I .32. . .). Example 1.2. Let b, = i(C,), where C,z denotes the circuit of length n. Then b, = 3, 6, = 2, b, = 5, and b,

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✍ Jiuqiang Liu πŸ“‚ Article πŸ“… 1994 πŸ› John Wiley and Sons 🌐 English βš– 387 KB πŸ‘ 2 views

## Abstract 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. ErdΓΆs, that the maximum number of m