Geodesic
Trees of Diameter $6$ and $7$ with Minimum Number of Independent Sets
Matematičeskie zametki, Tome 109 (2021) no. 2, pp. 276-289.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the problem of describing $n$-vertex trees of diameter $d$ containing as few independent sets as possible. This problem is solved for $d=6$ and $n>160$, as well as for $d=7$ and $n>400$.
Keywords: independent set, tree, diameter. 
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D. S. Taletskii. Trees of Diameter $6$ and $7$ with Minimum Number of Independent Sets. Matematičeskie zametki, Tome 109 (2021) no. 2, pp. 276-289. http://geodesic.mathdoc.fr/item/MZM_2021_109_2_a10/

[1] H. Prodinger, R. F. Tichy, “Fibonacci numbers of graphs”, Fibonacci Quart., 19:1 (1982), 16–21 | MR

[2] A. S. Pedersen, P. D. Vestergaard, “An upper bound on the number of independent sets in a tree”, Ars Combin., 84 (2007), 85–96 | MR

[3] A. B. Dainiak, Sharp Bounds for the Number of Maximal Independent Sets in Trees of Fixed Diameter, 2008, arXiv: 0812.4948

[4] A. Frendrup, A. S. Pedersen, A. A. Sapozhenko, P. D. Vestergaard, “Merrifield–Simmons index and minimum number of independent sets in short trees”, Ars Combin., 111 (2013), 85–95 | MR

[5] A. B. Dainyak, “O chisle nezavisimykh mnozhestv v derevyakh fiksirovannogo diametra”, Diskretn. analiz i issled. oper., 16:2 (2009), 61–73 | MR | Zbl