References
- H.A. Ahangar, M. Chellali, D. Kuziak, and V. Samodivkin, On maximal roman domination in graphs, Int. J. Comput. Math. 937 (2015), pp. 1093–1102. doi: 10.1080/00207160.2015.1052804
- H.A. Ahangar, T.W. Haynes, and J. Valenzuela-Tripodoro, Mixed roman domination in graphs, Bull. Malays. Math. Sci. Soc. 40(4) (2017), pp. 1443–1454. doi: 10.1007/s40840-015-0141-1
- H.A. Ahangar, M. Chellali, and S.M. Sheikholeslami, On the double roman domination in graphs, Discrete Appl. Math. 232 (2017), pp. 1–7. doi: 10.1016/j.dam.2017.06.014
- H.A. Ahangar, J. Amjadi, M. Chellali, S. Nazari-Moghaddam, and S. Sheikholeslami, Trees with double roman domination number twice the domination number plus two, Iran. J. Sci. Technol. Trans. A Sci. (2018). Available at https://doi.org/10.1007/s40995-018-0535-7.
- J. Amjadi, S. Nazari-Moghaddam, S.M. Sheikholeslami, and L. Volkmann, An upper bound on the double roman domination number, J. Combin. Optim. 36(1) (2018), pp. 81–89. doi: 10.1007/s10878-018-0286-6
- V. Anu and A. Lakshmanan, Double roman domination number, Discrete Appl. Math. 244 (2018), pp. 198–204. doi: 10.1016/j.dam.2018.03.026
- R.A. Beeler, T.W. Haynes, and S.T. Hedetniemi, Double roman domination, Discrete Appl. Math. 211 (2016), pp. 23–29. doi: 10.1016/j.dam.2016.03.017
- J. Bondy and U. Murty, Graph Therory, GTM 244, Springer-Verlag, New York, 2008.
- E. Castorini, P. Nobili, and C. Triki, Optimal routing and resource allocation in multi-hop wireless networks, Optim. Methods Softw. 23(4) (2008), pp. 593–608. doi: 10.1080/10556780801995907
- J. Cecílio, J. Costa, and P. Furtado, Survey on data routing in wireless sensor networks, in Wireless Sensor Network Technologies for the Information Explosion Era, Springer, Berlin, Heidelberg, 2010, pp. 3–46.
- E.W. Chambers, B. Kinnersley, N. Prince, and D.B. West, Extremal problems for roman domination, SIAM J. Discrete Math. 23(3) (2009), pp. 1575–1586. doi: 10.1137/070699688
- W.A. Chaovalitwongse, T.Y. Berger-Wolf, B. Dasgupta, and M.V. Ashley, Set covering approach for reconstruction of sibling relationships, Optim. Methods Softw. 22(1) (2007), pp. 11–24. doi: 10.1080/10556780600881829
- M. Chellali, T.W. Haynes, S.T. Hedetniemi, and A.A. McRae, Roman {2}-domination, Discrete Appl. Math. 204 (2016), pp. 22–28. doi: 10.1016/j.dam.2015.11.013
- M. Chlebík and J. Chlebíková, Approximation hardness of dominating set problems in bounded degree graphs, Inform. Comput. 206 (2008), pp. 1264–1275. doi: 10.1016/j.ic.2008.07.003
- E.J. Cockayne, P.A. Dreyer Jr, S.M. Hedetniemi, and S.T. Hedetniemi, Roman domination in graphs, Discrete Math. 278(1–3) (2004), pp. 11–22. doi: 10.1016/j.disc.2003.06.004
- B. Das and V. Bharghavan, Routing in ad-hoc networks using minimum connected dominating sets, 1997 IEEE International Conference Communications, 1997. ICC'97 Montreal, Towards the Knowledge Millennium, Montreal, Quebec, Canada, 1997, Vol. 1, pp. 376–380.
- G. Dobson, Worst-case analysis of greedy heuristics for integer programming with nonnegative data, Math. Oper. Res. 7(4) (1982), pp. 515–531. doi: 10.1287/moor.7.4.515
- P.A. Dreyer, Applications and variations of domination in graphs, Diss., Rutgers University, 2000.
- W. Goddard and M.A. Henning, Independent domination in graphs: A survey and recent results, Discrete Math. 313(7) (2013), pp. 839–854. doi: 10.1016/j.disc.2012.11.031
- A.A. Hagberg, D.A. Schult, and P.J. Swart, Exploring network structure, dynamics, and function using NetworkX, Proceedings of the 7th Python in Science Conference (SciPy2008), G. Varoquaux, T. Vaught, and J. Millman, eds., Pasadena, CA, 2008, pp. 11–15.
- M. Hajibaba and N.J. Rad, Some notes on the roman domination number and italian domination number in graphs, J. Phys. Conf. Ser. 890(1) (2017), p. 012123. IOP Publishing.
- G. Hao, X. Chen, and L. Volkmann, Double roman domination in digraphs, Bull. Malays. Math. Sci. Soc. 42(5) (2017), pp. 1907–1920. doi: 10.1007/s40840-017-0582-9
- S. Hedetniemi, P. Slater, and T.W. Haynes, Fundamentals of Domination in Graphs, CRC press, Boca Raton, FL, 2013.
- M.A. Henning, A survey of selected recent results on total domination in graphs, Discrete Math. 309(1) (2009), pp. 32–63. doi: 10.1016/j.disc.2007.12.044
- M. Ivanović, Improved mixed integer linear programing formulations for roman domination problem, Publ. Inst. Math. 99(113) (2016), pp. 51–58. doi: 10.2298/PIM1613051I
- H. Jiang, P. Wu, Z. Shao, Y. Rao and J. Liu, The double roman domination numbers of generalized petersen graphs P(n,2), Mathematics 6(10) (2018), pp. 206.
- Y. Ma, Q. Cai, and S. Yao, Integer linear programming models for the weighted total domination problem, Appl. Math. Comput. 358 (2019), pp. 146–150. doi: 10.1016/j.cam.2019.03.006
- H. Mercier, V.K. Bhargava, and V. Tarokh, A survey of error-correcting codes for channels with symbol synchronization errors, IEEE Commun. Surv. Tutor 12(1) (2010), pp. 87–96. doi: 10.1109/SURV.2010.020110.00079
- B.P. Mobaraky and S.M. Sheikholeslami, Bounds on Roman domination numbers of graphs, Mat. vesnik 60(4) (2008), pp. 247–253.
- N.J. Rad and H. Rahbani, Some progress on the double roman domination in graphs, Discuss. Math. Graph Theory 39(1) (2019), pp. 41–53. doi: 10.7151/dmgt.2069
- C.S. ReVelle and K.E. Rosing, Defendens imperium romanum: a classical problem in military strategy, Amer. Math. Monthly 107(7) (2000), pp. 585–594. doi: 10.1080/00029890.2000.12005243
- I. Stewart, Defend the roman empire!, Sci. Amer. 281(6) (1999), pp. 136–138. doi: 10.1038/scientificamerican1299-136
- M.K. Tural, Maximal matching polytope in trees, Optim. Methods Softw. 31(3) (2016), pp. 471–478. doi:10.1080/10556788.2015.1104679.
- L. Volkmann, Double roman domination and domatic numbers of graphs, Commun. Comb. Optim. 3 (2018), pp. 71–77.
- J. Yue, M. Wei, M. Li, and G. Liu, On the double roman domination of graphs, Appl. Math. Comput. 338 (2018), pp. 669–675.
- X. Zhang, Z. Li, H. Jiang, and Z. Shao, Double roman domination in trees, Inform. Process. Lett. 134 (2018), pp. 31–34. doi: 10.1016/j.ipl.2018.01.004