Geodesic
Bounds on the total double Roman domination number of graphs
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 4, pp. 1033-1061 Cet article a éte moissonné depuis la source Library of Science

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Let G be a simple graph with no isolated vertex and let γ_tdR(G) be the total double Roman domination number of G. In this paper, we present lower and upper bounds on γ_tdR(G) of a graph G in terms of the order, open packing number and the numbers of support vertices and leaves, and we characterize all extremal graphs. We also prove that for any connected graph G of order n with minimum degree at least two, γ_tdR(G)≤⌊4n3⌋.
Keywords: double Roman domination, total double Roman domination, open packing 
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Hao, Guoliang; Xie, Zhihong; Sheikholeslami, Seyed Mahmoud; Hajjari, Maryam. Bounds on the total double Roman domination number of graphs. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 4, pp. 1033-1061. http://geodesic.mathdoc.fr/item/DMGT_2023_43_4_a9/

[1] H. Abdollahzadeh Ahangar, J. Amjadi, M. Chellali, S. Nazari-Moghaddam and S.M. Sheikholeslami, Trees with double Roman domination number twice the domination number plus two, Iran. J. Sci. Technol. Trans. A Sci. 43 (2019) 1081–1088. https://doi.org/10.1007/s40995-018-0535-7

[2] H. Abdollahzadeh Ahangar, M. Chellali and S.M. Sheikholeslami, On the double Roman domination in graphs, Discrete Appl. Math. 232 (2017) 1–7. https://doi.org/10.1016/j.dam.2017.06.014

[3] J. Amjadi, S. Nazari-Moghaddam, S.M. Sheikholeslami and L. Volkmann, An upper bound on the double Roman domination number, J. Comb. Optim. 36 (2018) 81–89. https://doi.org/10.1007/s10878-018-0286-6

[4] J. Amjadi and M. Valinavaz, Relating total double Roman domination to 2-independence in trees, Acta Math. Univ. Comenian. (N.S.) LXXXIX (2020) 85–193.

[5] S. Banerjee, M.A. Henning and D. Pradhan, Algorithmic results on double Roman domination in graphs, J. Comb. Optim. 39 (2020) 90–114. https://doi.org/10.1007/s10878-019-00457-3

[6] R.A. Beeler, T.W. Haynes and S.T. Hedetniemi, Double Roman domination, Discrete Appl. Math. 211 (2016) 23–29. https://doi.org/10.1016/j.dam.2016.03.017

[7] X.-G. Chen, A note on the double Roman domination number of graphs, Czechoslovak Math. J. 70 (2020) 205–212. https://doi.org/10.21136/CMJ.2019.0212-18

[8] G. Hao, L. Volkmann and D.A. Mojdeh, Total double Roman domination in graphs, Commun. Comb. Optim. 5 (2020) 27–39.

[9] R. Khoeilar, M. Chellali, H. Karami and S.M. Sheikholeslami, An improved upper bound on the double Roman domination number of graphs with minimum degree at least two, Discrete Appl. Math. 270 (2019) 159–167. https://doi.org/10.1016/j.dam.2019.06.018

[10] N. Jafari Rad and H. Rahbani, Some progress on the double Roman domination in graphs, Discuss. Math. Graph Theory 39 (2019) 41–53. https://doi.org/10.7151/dmgt.2069

[11] A. Poureidi, On computing total double Roman domination number of trees in linear time, J. Algorithms Comput. 52 (2020) 131–137.

[12] Z. Shao, J. Amjadi, S.M. Sheikholeslami and M. Valinavaz, On the total double Roman domination, IEEE Access 7 (2019) 52035–52041. https://doi.org/10.1109/ACCESS.2019.2911659

[13] L. Volkmann, Double Roman domination and domatic numbers of graphs, Commun. Comb. Optim. 3 (2018) 71–77.

[14] X. Zhang, Z. Li, H. Jiang and Z. Shao, Double Roman domination in trees, Inform. Process. Lett. 134 (2018) 31–34. https://doi.org/10.1016/j.ipl.2018.01.004