[1] A. Rahmouni and M. Chellali, Independent Roman {2}-domination in graphs, Discrete Appl. Math., 236 (2018)
408–414.
[2] B. Courcelle, The monadic second-order logic of graphs. I. Recognizable sets of finite graphs, Inform. and Comput.,
85 (1990) 12–75.
[3] C. E. Leiserson, R. L. Rivest, T. H. Cormen and C. Stein, Introduction to algorithms, Second edition. MIT Press,
Cambridge, MA; McGraw-Hill Book Co., Boston, MA, 2001.
[4] C. S. ReVelle and K. E. Rosing, Defendens imperium romanum: a classical problem in military strategy, Amer.
Math. Monthly, 107 (2000) 585–594.
[5] C. Padamutham and V. S. R. Palagiri, Complexity Aspects of Variants of Independent Roman Domination in
Graphs, Bull. Iranian Math. Soc., (2021) 1715–1735.
[6] C. Padamutham and V. S. R. Palagiri, Algorithmic aspects of Roman domination in graphs, J. Appl. Math. Comput.,
64 (2020) 89–102.
[7] C. Padamutham and V. S. R. Palagiri, Complexity of Roman {2}-domination and the double Roman domination
in graphs, AKCE Int. J. Graphs Comb., 17 (2020) 1081–1086.
[8] D. A. Mojdeh and L. Volkmann, Roman {3}-domination (double Italian domination), Discrete Appl. Math., 283
(2020) 555–564.
[9] D. B. West, Introduction to Graph Theory, 2, Upper Saddle River: Prentice Hall, 2001.
[10] E. J. Cockayne, P. A. Dreyer, S. M. Hedetniemi and S. T. Hedetniemi, Roman domination in graphs, Discrete Math.,
278 (2004) 11–22.
[11] F. Alizade, H. R. Maimani, L. P. Majd and M. R. Parsa, Roman {2}-domination in graphs and graph products,
(2017).
[12] M. Adabi, E. E. Targhi, N. J. Rad and M. S. Moradi, Properties of independent Roman domination in graphs,
Australas. J. Combin., 52 (2012) 11–18.
[13] M. Chellali and N. J. Rad, Strong equality between the Roman domination and independent Roman domination
numbers in trees, Discuss. Math. Graph T., 33 (2013) 337–346.
[14] M. Chlebik and J. Chlebı́ková, The complexity of combinatorial optimization problems on d-dimensional boxes,
SIAM J. Discret. Math., 21 (2007) 158–169.
[15] M. Ivanović, Improved mixed integer linear programing formulations for roman domination problem, Publ. de
l’Institut Math., 99 (2016) 51–58.
[16] M. Chellali, T. W. Haynes, S. T. Hedetniemi and A. A. McRae, Roman {2}-domination, Discrete Appl. Math., 204
(2016) 22–28.
[17] M. R. Garey and D. S. Johnson, Computers and intractability. A guide to the theory of NP-completeness, A Series
of Books in the Mathematical Sciences, W. H. Freeman and Co., San Francisco, Calif., 1979.
[18] M. Yannakakis, Node- and edge-deletion NP-complete problems, In Proceedings of the Tenth Annual ACM Sympo-
sium on Theory of Computing, STOC, New York, USA, (1978) 253–264.
[19] N. Jafari Rad and L. Volkmann, Roman domination perfect graphs, An. Stiint. Univ. Ovidius Constanta Ser. Mat.,
19 (2011) 167–174.
[20] N. Mahadev and U. Peled, Threshold graphs and related topics, Annals of Discrete Mathematics, 56, North-Holland
Publishing Co., Amsterdam, 1995.
[21] O. Favaron, H. Karami, R. Khoeilar and S. M. Sheikholeslami, On the Roman domination number of a graph,
Discrete Math., 309 (2009) 3447–3451.
[22] P. Wu, Z. Li, Z. Shao and S. M. Sheikholeslami, Trees with equal Roman {2}-domination number and independent
Roman {2}-domination number, RAIRO-Oper. Res., 53 (2019) 389–400.
[23] R. Uehara and Y. Uno, Eﬃcient algorithms for the longest path problem, Algorithms and computation, Lecture
Notes in Comput. Sci., Springer, Berlin, (2004) 871–883.
[24] T. W. Haynes, S. Hedetniemi and P. Slater, Fundamentals of domination in graphs, Monographs and Textbooks in
Pure and Applied Mathematics, 208, Marcel Dekker, Inc., New York, 1998.
[25] T. W. Haynes, S. Hedetniemi and P. Slater, Domination in graphs: advanced topics, Marcel Dekker, 1997.