Domination parameters of generalized Sierpiński graphs

References

• Ahangar, H. A., Chellali, M, Sheikholeslami, S. M. (2017). On the double Roman domination in graphs. Discrete Appl. Math. 232: 1–7.
   Web of Science ®Google Scholar
• Alizadeh, F., Maimani, H. R., Majd, L. P, Parsa, M. R. (2022). Roman {2}-domination in graphs and graph products. Iran. J. Math. Sci. Inform. In Press.
   Google Scholar
• Amjadi, J., Nazari-Moghaddam, V., Sheikholeslami, S. M, Volkmann, L. (2018). An upper bound on the double Roman domination number. J. Comb. Optim. 36(6): 1–9.
   Google Scholar
• Anu, V, Aparna, L. S. (2018). Double Roman domination number. Discrete Appl. Math. 244: 198–204.
   Web of Science ®Google Scholar
• Anu, V, Aparna, L. S. (2021). Impact of some graph operators on double Roman domination number. Int. J. Comb. Graph Theory Appl. 6(1): 97–105.
   Google Scholar
• Anu, V, Aparna, L. S. (2020). The double Roman domination number of generalized Sierpiński graphs. Discrete Math. Algorithms Appl. 12(4): Article 2050047.
   Web of Science ®Google Scholar
• Aparna, L. S, Amala, B. (2022). Variations of Roman domination in Kneser graphs. Manuscript.
   Google Scholar
• Balakrishnan, R, Ranganathan, K. (1999). A Text Book of Graph Theory. New York: Springer.
   Google Scholar
• Beeler, R. A., Haynes, T. W, Hedetniemi, S. T. (2016). Double Roman domination. Discrete Appl. Math. 211(1): 23–29.
   Google Scholar
• Chellali, M., Haynes, T. W., Hedetniemi, S. T, McRae, A. A. (2016). Roman {2}-domination. Discrete Appl. Math. 204: 22–28.
   Web of Science ®Google Scholar
• Chellai, M., Rad, N. J., 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 II. AKCE Int. J. Graphs Comb. 17(3): 966–984.
   Web of Science ®Google Scholar
• Chellai, M., Rad, N. J., Sheikholeslami, S. M, Volkmann, L. (2021). Varieties of Roman Domination, Structures of Domination in Graphs. In: Haynes, T.W., Hedetniemi, S.T., Henning, M. A., eds. Topics in Domination in Graphs. Berlin/Heidelberg: Springer, pp. 273–307.
   Google Scholar
• Cockayne, E. J., Dreyer, P. A., Jr, Hedetniemi, S. M, Hedetniemi, S. T. (2004). Roman domination in graphs. Discrete Math. 278: 1–3.
   Web of Science ®Google Scholar
• Deepalakshmi, J., Marimuthu, G., Somasundaram, A, Arumugam, S. (In press). Domination parameters of a splitting graph of a graph. Commun. Comb. Optim.
   Google Scholar
• Desormeaux, W. J., Haynes, T. W, Henning, M. A. (2018). Domination parameters of a graph and its complement. Discuss. Math. Graph Theory 38(1): 203–215.
   Web of Science ®Google Scholar
• Gao, H., Xi, C., Li, K., Zhang, Q, Yang, Y. (2019). The Italian domination number of generalized Petersen graphs P(n,3). Mathematics 7(8): 714. Article 714.
   Web of Science ®Google Scholar
• Gao, H., Xu, T, Yang, Y. (2019). Bagging approach for Italian domination in Cn□Pm. IEEE Access.
   Web of Science ®Google Scholar
• Gravier, S., Kovše, M, Parreau, A. (2011). Generalized Sierpinski Graphs 1. https://www.semanticscholar.org/paper/Generalized-Sierpinski-graphs-1-Gravier-Kovse/3c21ce24174d1cdf788e2988702c1e81dc686436.
   Google Scholar
• Hajibaba, M, Rad, N. J. (2019). On domination, 2-domination and Italian domination numbers. Util. Math. 111: 271–280.
   Web of Science ®Google Scholar
• Hao, G., Chen, X, Volkmann, L. (2019). Double Roman domination in digraphs. Bull. Malays. Math. Sci. Soc. 42(5): 1907–1920.
   Web of Science ®Google Scholar
• Haynes, T. W., Henning, M. A, Volkman, L. (2020). Graphs with large Italian domination number. Bull. Malays. Math. Sci. Soc. 43(6): 4273–4287.
   Web of Science ®Google Scholar
• Haynes, T. W, Henning, M. A. (2019). Perfect Italian domination in trees. Discrete Appl. Math. 260: 164–177.
   Web of Science ®Google Scholar
• Henning, M. A, Klostermeyer, W. F. (2017). Italian domination in trees. Discrete Appl. Math. 217: 557–564.
   Web of Science ®Google Scholar
• Hinz, A. M., Klavžar, S, Zemljicˇ, S. S. (2017). A survey and classification of Sierpiński-type graphs. Discrete Appl. Math. 217: 565–600.
   Web of Science ®Google Scholar
• Jismy, V, Aparna, L. S. (2022). Impact of vertex addition on Italian domination number. Indian J. Discrete Math. 8(1): 11–20.
   Google Scholar
• Jismy, V., Anu, V, Aparna, L. S. (2021). Italian domination and perfect Italian domination on Sierpiński graphs. J. Discrete Math. Sci. Cryptogr. 24(7): 1885–1894.
   Web of Science ®Google Scholar
• Jismy, V, Aparna, L. S. (2021). Italian domination on Mycielskian and Sierpiński graphs. Discrete Math. Algorithms Appl. 13(4): Article 2150037.
   Google Scholar
• Jismy, V, Aparna, L. S. (2022). Perfect Italian domination number of graphs. Palest. J. Math. 11(1): 260–270.
   Google Scholar
• Klavžar, S, Milutinović, U. (1997). Graphs S(n,k) and a variant of the tower of Hanoi problem. Czechoslov. Math. J. 47(1): 95–104.
   Web of Science ®Google Scholar
• Klavžar, S., Milutinović, U, Petr, C. (2002). 1-Perfect codes in Sierpiński graphs. Bull. Austral. Math. Soc. 66(3): 369–384.
   Web of Science ®Google Scholar
• Lauri, J, Mitillos, C. (2020). Perfect Italian domination on planar and regular graphs. Discrete Appl. Math. 285: 676–687.
   Web of Science ®Google Scholar
• Liu, C. A. (2020). Domination in Sierpiński Graphs S(Kn,t). arXiv:2008.09807v1.
   Google Scholar
• Mojdeh, D. A., Masoumi, I, Volkman, L. (2022). Restrained double Roman domination of a graph. RAIRO-Oper. Res. 56(4): 2293–2304.
   Web of Science ®Google Scholar
• Poureidi, A, Rad, N. J. (2020). On the algorithmic complexity of Roman {2}-domination. Iran. J. Sci. Technol. Trans. Sci. 44(3): 791–799.
   Web of Science ®Google Scholar
• Poklukar, D. R, Zerovnik, J. (2022). On the double Roman domination in generalized Petersen graphs P(5k,k). Mathematics 10(1): Article 119.
   Web of Science ®Google Scholar
• Ramezani, F., Rodríguez-Bazan, E. D, Rodríguez-Velázquez, J. A. (2017). On the Roman domination number of generalized Sierpiński graphs. Filomat 31(20): 6515–6528.
   Web of Science ®Google Scholar
• Yang, H, Zhou, X. (2020). Some properties of double Roman domination. Discrete Dyn. Nat. Soc. 2020: 1–5. Article 6481092.
   Web of Science ®Google Scholar