On [k] -Roman domination in graphs

References

• Abdollahzadeh Ahangar, H., Álvarez, M. P., Chellali, M., Sheikholeslami, S. M., Valenzuela-Tripodoro, J. C. (2021). Triple Roman domination in graphs. Appl. Math. Comput. 391: 125444.
   Web of Science ®Google Scholar
• Abdollahzadeh Ahangar, H., Amjadi, J., Atapour, M., Chellali, M., Sheikholeslami, S. M. (2019). Double Roman trees. Ars Combin. 145: 173–183.
   Google Scholar
• Abdollahzadeh Ahangar, H., Amjadi, J., Chellali, M., Nazari-Moghaddam, S., Sheikholeslami, S. M. (2019). Trees with double Roman domination number twice the domination number plus two. Iran. J. Sci. Technol. Trans. A Sci. 43: 1081–1088 .
   Web of Science ®Google Scholar
• Abdollahzadeh Ahangar, H., Chellali, M., Sheikholeslami, S. M. (2019). On the double Roman domination in graphs. Discrete Appl. Math. 103: 1–11.
   Google Scholar
• Abdollahzadeh Ahangar, H., Chellali, M., Sheikholeslami, S. M. (2020). Outer independent double Roman domination. Appl. Math. Comput. 364: Article ID: 124617.
   Web of Science ®Google Scholar
• Abdollahzadeh Ahangar, H., Chellali, M., Sheikholeslami, S. M., Valenzuela-Tripodoro, J. C. (2022). Maximal double Roman domination in graphs. Appl. Math. Comput. 414: Article ID: 126662.
   Web of Science ®Google Scholar
• Amjadi, J., Khalili, N. (2022). Quadruple Roman domination in graphs. Discrete Math. Algorithms Appl. 14: Article ID: 2150130.
   Web of Science ®Google Scholar
• Amjadi, J., Khalili, N. (2023). New results on quadruple Roman domination in graphs. Discrete Math. Algorithms Appl. 15: Article ID: 2250078.
   Google Scholar
• Beeler, R. A., Haynes, T. W., Hedetniemi, S. T. (2016). Double Roman domination. Discrete Appl. Math. 211: 23–29.
   Web of Science ®Google Scholar
• Chellali, M., Jafari Rad, N., Sheikholeslami, S. M., Volkmann, L. (2020). Roman domination in graphs. In: Haynes, T. W., Hedetniemi, S. T., Henning, M. A., eds. Topics in Domination in Graphs. Berlin/Heidelberg: Springer, pp. 365–409.
   Google Scholar
• Chellali, M., Jafari Rad, N., Sheikholeslami, S. M., Volkmann, L. (2020). Varieties of Roman domination. In: Haynes, T. W., Hedetniemi, S. T., Henning, M. A., eds. Structures of Domination in Graphs. Berlin/Heidelberg: Springer, pp. 273–307.
   Google Scholar
• Chellali, M., Jafari Rad, N., Sheikholeslami, S. M., Volkmann, L. (2020). Varieties of Roman domination II. AKCE Int. J. Graphs Comb. 17: 966–984.
   Web of Science ®Google Scholar
• Chellali, M., Jafari Rad, N., Sheikholeslami, S. M., Volkmann, L. (2022). The Roman domatic problem in graphs and digraphs: A survey. Discuss. Math. Graph Theory 42: 861–891.
   Web of Science ®Google Scholar
• Chellali, M., Jafari Rad, N., Sheikholeslami, S. M., Volkmann, L. (2020). A survey on Roman domination parameters in directed graphs. J. Combin. Math. Combin. Comput. 115: 141–171.
   Google Scholar
• Cockayne, E. J., Dreyer, P. A., Hedetniemi, S. M., Hedetniemi, S. T. (2004). Roman domination in graphs. Discrete Math. 278: 11–22.
   Web of Science ®Google Scholar
• Hajjari, M., Abdollahzadeh Ahangar, H., Khoeilar, R., Shao, Z., Sheikholeslami, S. M. (2023). An upper bound on triple Roman domination. Commun. Comb. Optim. 8: 505–511.
   Google Scholar
• Khoeilar, R., Chellali, M., Karami, H., Sheikholeslami, S. M. (2019). An improved upper bound on the double Roman domination number of graphs with minimum degree at least two. Discrete Appl. Math. 270: 159–167.
   Web of Science ®Google Scholar
• Kou, Z., Kosari, S., Hao, G., Amjadi, J., Khalili, N. (2021). Quadruple Roman domination in trees. Symmetry 13: Article ID: 1318.
   Google Scholar
• Li, X. Z., Jiang, H., Shao, Z. (2018). Double Roman domination in trees. Inform. Process. Lett. 134: 31–34.
   Web of Science ®Google Scholar
• Maimani, H. R., Momeni, M., Rahimi Mahid, F., Sheikholeslami, S. M. (2020). Independent double Roman domination in graphs. AKCE Int. J. Graphs Combin. 17: 905–910.
   Web of Science ®Google Scholar
• Poureidi, A. (2023). Double Roman domination in graphs: algorithmic complexity. Commun. Comb. Optim. 8: 491–503.
   Google Scholar
• Poureidi, A., Fathali, J. Algorithmic complexity of triple Roman dominating functions on graphs. Commun. Comb. Optim. (in press)
   Google Scholar
• Rahmouni, A., Abdollahzadeh Ahangar, H., Chellali, M., Sheikholeslami, S. M. (2022). Further results on independent double Roman trees. AKCE Int. J. Graphs Combin. 19: 311–315.
   Web of Science ®Google Scholar
• Rupnik Poklukar, D., Žerovnik, J. (2023). Double Roman domination: a survey. Mathematics 11: Article ID: 351.
   Web of Science ®Google Scholar
• Teymourzadeh, A., Mojdeh, D. A. (2023). Covering total double Roman domination in graphs. Commun. Comb. Optim. 8: 115–125.
   Google Scholar