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English version:
Journal of Applied and Industrial Mathematics, 2020, 14:1, 131-147

Volume 27, No 1, 2020, P. 61-87

UDC 519.172.1
A. D. Kurnosov
The set of all values of the domination number in trees with a given degree sequence

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.
Illustr. 1, bibliogr. 12.

Keywords: degree sequence, tree, domination number, inverse problem, realization, realization tree.

DOI: 10.33048/daio.2020.27.656

Artem D. Kurnosov 1
1. Moscow Institute of Physics and Technology,
9 Institutskii Lane, 9, 141700 Dolgoprudnyi, Russia
e-mail: kurnosov@phystech.edu

Received April 6, 2019
Revised August 21, 2019
Accepted August 28, 2019

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