Geodesic
Trees with a given number of leaves and the maximal number of maximum independent sets
Diskretnaya Matematika, Tome 32 (2020) no. 2, pp. 71-84

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A complete description of trees with maximal possible number of maximum independent sets among all $n$-vertex trees with exactly $l$ leaves is obtained. For all values of the parameters $n$ and $l$ the extremal tree is unique and is the result of merging the endpoints of $l$ simple paths.
Keywords: independent set, maximum independent set, maximal independent set, extremal tree. 
@article{DM_2020_32_2_a5,
     author = {D. S. Taletskii and D. S. Malyshev},
     title = {Trees with a given number of leaves and the maximal number of maximum independent sets},
     journal = {Diskretnaya Matematika},
     pages = {71--84},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2020_32_2_a5/}
}
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D. S. Taletskii; D. S. Malyshev. Trees with a given number of leaves and the maximal number of maximum independent sets. Diskretnaya Matematika, Tome 32 (2020) no. 2, pp. 71-84. http://geodesic.mathdoc.fr/item/DM_2020_32_2_a5/