Geodesic
On the number of independent sets in graphs with fixed independence number
Diskretnaya Matematika, Tome 19 (2007) no. 2, pp. 63-66

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We construct a sequence of graphs of large degree with growing number of vertices for which the number of independent sets is substantially greater than the number of all subsets of the independent set of maximal cardinality. 
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     author = {A. B. Dainiak},
     title = {On the number of independent sets in graphs with fixed independence number},
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A. B. Dainiak. On the number of independent sets in graphs with fixed independence number. Diskretnaya Matematika, Tome 19 (2007) no. 2, pp. 63-66. http://geodesic.mathdoc.fr/item/DM_2007_19_2_a5/