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English version: Journal of Applied and Industrial Mathematics, 2020, 14:1, 131-147 |
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Volume 27, No 1, 2020, P. 61-87 UDC 519.172.1
Keywords: degree sequence, tree, domination number, inverse problem, realization, realization tree. DOI: 10.33048/daio.2020.27.656 Artem D. Kurnosov 1 Received April 6, 2019 References[1] R. Diestel, Graph Theory (Springer, Heidelberg, 2016).[2] V. A. Emelichev, O. I. Melnikov, V. I. Sarvanov, and R. I. Tyshkevich, Lectures on Graph Theory (Nauka, Moscow, 1990; B. I. Wissenschaftsverlag, Mannheim, 1994). [3] T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). [4] A. B. Dainyak and A. D. Kurnosov, On an extremal inverse problem in graph theory, Diskretn. Anal. Issled. Oper. 22 (1), 19–30 (2015) [J. Appl. Ind. Math. 9 (2), 157–164 (2015)]. [5] V. Havel, A remark on the existence of finite graphs, Cas. Pestování Mat. 80 (4), 477–480 (1955). [6] S. Hakimi, On the realizability of a set of integers as degrees of the vertices of a graph, SIAM J. Appl. Math. 10, 496–506 (1962). [7] O. Favaron, A bound on the independent domination number of a tree, Vishwa Int. J. Graph Theory 1 (1), 19–27 (1992). [8] M. Gentner, M. Henning, and D. Rautenbach, Largest domination number and smallest independence number of forests with given degree sequence, Discrete Appl. Math. 206, 181–187 (2016). [9] M. Gentner, M. Henning, and D. Rautenbach, Smallest domination number and largest independence number of graphs and forests with given degree sequence, J. Graph Theory 88 (1), 131–145 (2018). [10] M. Lemanska, Lower Bound on the Domination Number of a Tree, Discuss. Math., Graph Theory 24, 165–169 (2004). [11] P. J. Slater, Locating dominating sets and locating-dominating sets, in Graph Theory, Combinatorics and Applications (Proc. 7th Quadrennial Int. Conf. Theory and Applications of Graphs, Kalamazoo, USA, June 1–5, 1992), Vol. 2 (Wiley, New York, 1995), pp. 1073–1079. [12] W. J. Desormeaux, T. W. Haynes, and M. A. Henning, Improved bounds on the domination number of a tree, Discrete Appl. Math. 177, 88–94 (2014). |
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