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The Set of All Values of the Domination Number in Trees with a Given Degree Sequence

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Abstract

We find the set of all values of the domination number for a class of trees with some given vertex degrees that forms a segment of naturals. We prove that each intermediate value of the segment can be obtained by gradually changing the tree that minimizes the domination number and with the use of two special operations, so that the last tree maximizes the domination number.

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Acknowledgments

The author expresses his indebtedness to A. B. Dainyak for the numerous discussions that led to improvement of exposition.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700, Russia

    A. D. Kurnosov

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  1. A. D. Kurnosov
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Correspondence to A. D. Kurnosov.

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Russian Text © The Author(s), 2020, published in Diskretnyi Analiz i Issledovanie Operatsii, 2020, Vol. 27, No. 1, pp. 61–87.

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Kurnosov, A.D. The Set of All Values of the Domination Number in Trees with a Given Degree Sequence. J. Appl. Ind. Math. 14, 131–147 (2020). https://doi.org/10.1134/S1990478920010135

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  • DOI: https://doi.org/10.1134/S1990478920010135

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