Geodesic
Bounds on the global double Roman domination number in graphs
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 2, pp. 539-554 Cet article a éte moissonné depuis la source Library of Science

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Let G be a simple graph of order n and let γ_gdR(G) be the global double Roman domination number of G. In this paper, we give some upper bounds on the global double Roman domination number of G. In particular, we completely characterize the graph G with γ_gdR(G)=2n-2 and γ_gdR(G)=2n-3. Our results answer a question posed by Shao et al. (2019).
Keywords: global double Roman domination, double Roman domination, complement 
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Hao, Guoliang; Wei, Shouliu; Sheikholeslami, Seyed Mahmoud; Chen, Xiaodan. Bounds on the global double Roman domination number in graphs. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 2, pp. 539-554. http://geodesic.mathdoc.fr/item/DMGT_2024_44_2_a6/

[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.M. Sheikholeslami and L. Volkmann, Global rainbow domination in graphs, Miskolc Math. Notes 17 (2016) 749–759. https://doi.org/10.18514/MMN.2017.1267

[4] M. Atapour, S.M. Sheikholeslami and L. Volkmann, Global Roman domination in trees, Graphs Combin. 31 (2015) 813–825. https://doi.org/10.1007/s00373-014-1415-3

[5] 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

[6] X. 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

[7] W.J. Desormeaux, P.E. Gibson and T.W. Haynes, Bounds on the global domination number, Quaest. Math. 38 (2015) 563–572. https://doi.org/10.2989/16073606.2014.981728

[8] G. Hao and X. Chen, On the global double Roman domination of graphs, Bull. Malays. Math. Sci. Soc. 43 (2020) 3007–3018. https://doi.org/10.1007/s40840-019-00851-4

[9] G. Hao, K. Hu, S. Wei and Z. Xu, Global Italian domination in graphs, Quaest. Math. 42 (2019) 1101–1115. https://doi.org/10.2989/16073606.2018.1506831

[10] G. Hao, L. Volkmann and D.A. Mojdeh, Total double Roman domination in graphs, Commun. Comb. Optim. 5 (2020) 27–39. https://doi.org/10.22049/CCO.2019.26484.1118

[11] 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

[12] P.R.L. Pushpam and S. Padmapriea, Global Roman domination in graphs, Discrete Appl. Math. 200 (2016) 176–185. https://doi.org/10.1016/j.dam.2015.07.014

[13] E. Sampathkumar, The global domination number of a graph, J. Math. Phys. Sci. 23 (1989) 377–385.

[14] Z. Shao, S.M. Sheikholeslami, S. Nazari-Moghaddam and S. Wang, Global double Roman domination in graphs, J. Discrete Math. Sci. Cryptogr. 22 (2019) 31–44. https://doi.org/10.1080/09720529.2019.1569833

[15] L. Volkmann, Double Roman domination and domatic numbers of graphs, Commun. Comb. Optim. 3 (2018) 71–77. https://doi.org/10.22049/cco.2018.26125.1078

[16] 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