Abstract
A few lower bounds are obtained for the number of independent sets in the trees of diameter 6, 7, 8, and 9. Some characteristic is given of the extreme trees of an arbitrary diameter.
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A. B. Dainiak, “Sharp Bounds for the Number of Maximal Independent Sets in Trees of Fixed Diameter,” arXiv:0812.4948v1.
A. Frendrup, A. S. Pedersen, A. A. Sapozhenko, and P. D. Vestergaard, Merrifield-Simmons Index and Minimum Number of Independent Sets in Short Trees, Research Report Series, ISSN 1399-2503, R-2009-03 (Department of Mathematical Sciences, Aalborg Univ., 2009).
A. S. Pedersen and P. D. Vestergaard, “An Upper Bound on the Number of Independent Sets in a Tree,” Ars Combinatoria 84, 85–96 (2007).
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Original Russian Text © A.B. Dainyak, 2009, published in Diskretnyi Analiz i Issledovanie Operatsii, 2009, Vol. 16, No. 2, pp. 61–73.
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Dainyak, A.B. On the number of independent sets in the trees of a fixed diameter. J. Appl. Ind. Math. 4, 163–171 (2010). https://doi.org/10.1134/S1990478910020043
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DOI: https://doi.org/10.1134/S1990478910020043